Dorothea Burstyn's article on punch ladles (#67 Let’s drink and be merry - a study about punch ladles) mentions a fascinating sub-set with inset coins.
Can we use the coins better to date the ladles, why were the coins used, what coins were used?
I'll first offer my hypotheses and some observations on collecting. I'll follow with opinions solicited from reputable collectors and dealers in silver and coins.

Georgian coins:

The standard reference for British coins is:
Coins of England and the United Kingdom
by Philip Skingley (Editor) Publisher: Spink & Son Ltd, 2007 - ISBN 1902040821

The Georgian kings of England were:

The three metals used are gold, silver and copper. We need only concern ourselves with the precious metals. I cannot definitively state copper coins would not have been used, but it seems, unless there were some overwhelming personal reason, there’d be no point setting base within precious metal.
As far as I know, the coins of the period are dated but not denominated. It appears size and the verso design are the governing factors, not surprising since much of the population was illiterate. I find this confounding because the catalog does not give clear size indications. Lest we feel sanctimonious, look closely at U.S. coinage - no numbered value appears. If the bearer cannot read the lingua franca, lots of luck.
I think identifying the coins employed adds to the description of the ladle, and gives some possible indication as to value, especially if they are gold, with the caveat a coin thus set would be considered worthless to numismatists. Since there seems to be no record of the quantities issued, the catalog value of the coin appears related to the rarity and provides some clue as to the likelihood of particular dates appearing.
The availability of precious metal is related to the issuance of coins and, incidentally, the weight and amount of silver objects (note 1):

In 1723 a large quantity of silver was brought to the mint by the South Sea Company to be made into coin…The gold coins of George II were given new reverses….This finally stopped the fraudulent gilding of silver coins, a practice which was very common during this period…In 1744 Admiral Anson returned to England…with an immense quantity of bullion…Most of Anson’s treasure consisted of Spanish-American silver coin, though there was some gold…After 1745, however, it appears that the supply of silver from home sources failed due to the exhaustion of the mines…there were further issues of silver coin in 1750, 1751, 1757, 1758…Owing to the increasing difficulty in obtaining silver, and consequent increase in its price, the 1758 coins were the last silver coins issued in any quantity for nearly thirty years…[In George III’s reign] even gold became so scarce during the Napoleonic Wars that a paper currency more or less took its place…The issue of guineas was interrupted in 1797 owing to the hazards of importing gold bullion from overseas during the Napoleonic Wars…Owing to the shortage of gold, bank-notes were declared legal tender in 1797 for any amounts over one pound, and so from that time until the great re-coinage of 1816/17, the country’s finances were run more or less on paper currency. Owing to the high price of silver no silver coins were issued during the earlier part of George III’s reign except for small amounts of “Maundy” coins and a very limited quantity of shillings dated 1763…No other silver coins were struck until the year 1757, when, following a temporary fall in the high price of silver, a very large number of shillings and six-pences were issued…A number of private silver tokens began to appear in 1811, being issued by local authorities, private traders and bankers…Though the issuing of these tokens was a breach of the authorities took no action against the issuers as they did serve some useful purpose…in 1813, all private silver tokens were prohibited.

Most of the people in Georgian England never handled banknotes. The wages for the servant classes for an entire quarter was usually less than the smallest denomination notes. The coins, as follows, were used for nearly all transactions until the wars with Revolutionary France caused a hard currency shortage.

Not all coin denominations were minted every year especially after 1797 when the bullion needed for coins were also needed for the war efforts against Revolutionary France. This bullion shortage continued through the wars until after Waterloo (note 2).

The relation of the date of the coin to the date of the ladle:

We can take the date of the coin as a terminus post quem, but how long after might the ladle date? Being mindful of the erratic issuance of coinage, we can locate the next issuance but that only tells us fresh coins were unavailable during a certain gap.
Some speculate the ladles are close to the date of the coin. One dealer writes:

By and large it seems to be accepted in auction rooms that this type of ladle is contemporary to the date of the coin…Of course destroying the coin of the realm in this manner was illegal so no hallmarking could be done and without hallmarks it is impossible to put an exact date on it.

My experience with auctioneers is mixed; Christies, sure, but ordinary auctioneers? I think it’s more likely the ladle manufacture would be near the coin date but not conclusively. In the absence of other cues the auctioneer's assumption is useful. But, coins remain in circulation a long time, might be stored and used later, and as noted above there were long periods of no new coins.

Maybe the coin would reflect some personal connection with the owner: People buy silver with their initials. I can imagine someone presenting a smith with a coin dating from his mother’s natal year and asking to imbed it, or a signal event in the nation’s history, or a good luck coin.

I think dating might rely more on characteristics of the ladle itself (see Ms. Burstyn’s article). While many ladles are not dated, and with coin ladles a case is made that it’s not to offer evidence to the Crown, an absence of stamps is common in these as well as other articles. There are, as well, examples of hallmarked coin ladles. I have been unable to find the statutes governing destroying coinage so cannot have an opinion.

Here’s a ladle from my collection, not a coin ladle, but instructive as to dating. The format and repousse appear 1750 - 1775 (always acknowledging retardataire possibilities). We have a satisfying conjunction of elements: design, lettering style and marks. A 1776 date stamp, the stamp of Thomas Shepherd (1st mark 1769, 5th mark 1786), and an inscribed date of 1779 in period style. Doesn’t get any better than that.

A 1776 silver ladle (no coin)	detail

Some examples of coins in ladles: silver, gold-plated silver, gold

It's been said smiths used coins when the value of the silver in the coins exceeded the face value and was higher than market silver, and that smiths beat coins into bowls. The central coin would be unbeaten filler. It’s incontrovertible that coins were beaten into bowls because some bowls retain the coin impress.

A 1757 silver shilling ladle	detail

A 1757 silver shilling ladle. It would be far easier to convert a quantity of coins into stock. Imagine what would be involved in beating a round coin to form a bowl, cutting a hole and soldering another coin in the center. Further, the thickness of the central coin would be greater than the surround, and thus more valuable. If the goal is to minimize cost, why not beat that out as well? I suspect while using coins for raw material occurred it's far more likely the coins were a decorative element, a practice that continued until the current era, I suspect through intervals where arbitrage was not a consideration.

A 1787 gold-plated silver shilling ladle, fully hallmarked for 1807	1787 gold-plated silver shilling

A 1787 gold-plated silver shilling ladle, fully hallmarked for 1807 (from my collection). The maker’s mark is undecipherable. This is an example that challenges the assertion the use of coins in Georgian ladles was illegal. A fuller discussion of this controversy follows.

Another 1787 gold-plated silver shilling ladle, fully hallmarked for 1807	1787 gold-plated silver shilling

A second example of a fully hallmarked coin ladle. The date stamp is for 1807, the maker’s mark obscured. Clearly by this time makers were stamping their coin-embedded labels. It may be that the laws against using coins thusly never existed, weren’t enforced, or were repealed by this time.

Elizabeth II, hallmarked Sheffield 1976	10 New Pence

Elizabeth II, hallmarked Sheffield 1976. In this case we have a coin captured in a ladle that’s fully hallmarked. May we assume the manufacturers of this label knew there was no breach of the law? Where does that leave the injunction against defacing currency? Did it exist? If so, was it rescinded?

An 1808 gold half guinea mis-identified as a "solid gold George III shilling coin"

Gold coins are far more valuable than silver coins, and discredit the theory of using coinage to save raw material cost. In this case an 1808 gold half guinea was mis-identified as a "solid gold George III shilling coin": Silver shillings were sometimes gold plated by individuals for enhancement or fraud (note 3).
A coin dealer writes, "I have seen many of these shillings that were gilded because they were the same size as a gold guinea". Another coin dealer, "Coins of this period were quite often Gilt, and used as good luck charms, or keepsakes".
The plating may be pristine or worn. Sometimes the lighting may make silver appear gold, but when it's embedded in silver, as in this worn example, the distinction is obvious (note 3)

1757 gold-plated shilling

1757 gold-plated shilling, ladle in my collection

Another example (date unknown)

An example of an advertisement where the photograph is too small to read the date on the coin

A ladle incorporating an 1813 Irish token

An example of ladle incorporating an 1813 Irish token

What to look for in buying coin ladles

Condition is always important. These objects may have been in use for hundreds of years. Where might stress and have contact occurred?

Points of special focus include:

1 Socket joint damage may appear on either side of the connection to the bowl, evidenced by subsequent solder. If the solder is clean, solid and well done, I don’t find this objectionable. The interior joint area may be covered with a decorative cut piece. If there’s no cut piece check it’s not missing, as revealed by evidence of solder and disrupted patterning.

2 The handle should fit securely into the socket. Note how in this illustration the handle appears wider than the socket where they meet and is shorter than the norm probably indicating it has been cut down and reset

It isn’t unusual that the handle becomes loose. I repaired a detached baleen handled ladle, cutting out the silver rivet, grinding and scraping out the remnants of baleen in the socket, and reshaping the butt of the handle. I could have used a full dental kit.

3 As with the socket and stem, the cap should be secure (not all ladles have caps).

4 The handle may be of wood, baleen, ivory or other bone. An expert writes:
The "horn" handles they talk about in Canada are almost certainly baleen. Not sure what kind of cow had a horn that could be manhandled into a twisted ladle handle. Perhaps "horn" is a way of avoiding CITES restrictions on international baleen sales. Most if not all British baleen of the 18th-century came from the seasonal Greenland Right Whale (Bowhead) fishery of the eastern arctic. Baleen strips were extracted, bundled, and taken home for further refinement.
Look for unsightly, unstable cracks and any evidence of replacement. Baleen, which must be twisted into shape may revert and cannot easily be reconstituted. As with other objects that take vigorous use, e.g. fish slices, it’s possible the handle is a replacement as well as being cut down.

5 Monograms and crests can be removed, or removed and replaced by later owners. Erasure results in thinning of the silver. You may see awkward patches inside or out, solder, scratches. Sometimes the patch may be skillfully incorporated into a cartouche, more often it is too apparent. Breathing over the area may reveal changes in condensation patterns. Subsequent changes usually devalues a piece, but if it’s skillful I am not troubled.

Finally, dealers may blithely advise that damage can easily be repaired by a competent silversmith. The only reputable silversmith I know is an hour and one half round trip. He will conjecture, but not firmly estimate, on the basis of photographs meaning I’d have to buy an object before I’d have a reliable idea of the repair cost. Further, I would not know if the repair would be acceptable to me. The rough estimates I’ve solicited have been more than the cost of the object. I would only entertain a repair if I could not do without something and its value was far greater than that of the contemplated repair.