One of your correspondents mentions the 1820 half crown as the last time a British monarch appeared on a coin dated in the year of accession. Let me offer a little further information.

The half crown (two shillings and sixpence, or an eighth of a pound) was not struck in the first 56 years of George III's reign, when little silver was issued, but with the Great Recoinage of 1816, it appeared again. It was apparently quite popular at the time: Almost 16 million were struck between 1816 and 1819. Nearly 32 million shillings were struck over the same span, and the sixpence was also heavily struck, but the greatest amount of silver was used for half crowns. Only about 800,000 crowns were struck in the same period. The half crown was therefore the largest silver coin with wide circulation. It was also close in size and value to the three-shilling token issued by the Bank of England between 1811 and 1816 because of the coin shortage.

King George III died on January 20, 1820. The Royal Mint kept working with whatever dies it had as Benedetto Pistrucci and others began preparations for the new reign's coinage. Silver shillings and sixpences were struck with George III's head, as were the Maundy denominations of one through four pence.

Except possibly with an 1819 date (the using up of old dies in a later year was not unknown in an era when dies required considerable labor), no George III half crowns were struck in 1820. Howard Linecar's (p. 97) tells us We find in "Annals Of The Coinage Of Great Britain And Its Dependencies, Volume 2, by Rogers Ruding (1840 edition, available on Google Books) the following entry under 1820:

No matching entry for the other silver coins appears until February 23, 1821.

On October 20, 1820, George IV issued a proclamation (printed in the following day's London Gazette) reciting the authority for issuing the coins, describing them, and stating that the issue "has been delivered from Our Mint to the Bank of England, and will be issued therefrom for the use of Our subjects and that the new half crown be

These were not the first George IV coins struck by the Royal Mint: Ruding tells us that in April, coins were authorized for Mauritius. These, known as , bear George IV's name and titles but not his portrait.

The question is, why were the 1820 half crowns struck? I don't find a written answer but most likely because commerce would not wait until 1821 for these important coins to be issued.

To read the earlier E-Sylum article, see:
DOES THE CHARLES III COIN BREAK TRADITION?(https://www.coinbooks.org/v25/esylum_v25n41a07.html)