Smaller coins have lower value than larger coins of the same metal. There are several types of coin that are quite small, even those currently in circulation. The 5p coin in modern British money isn't quite that small, but it's still pretty small, at 18mm diameter - half as much again in diameter as the coins you're talking about. In Euros, the one cent coin is slightly smaller, at 16.25mm.

If we look at British coinage of the pre-decimal age, the Three-halfpence (1.5p) was a silver coin of 12mm diamater, used in the 19th century. The quarter-farthing, worth one sixteenth of a penny, was not much larger at 13.5mm. This was also used in the 19th century. A silver thruppence, in use until 1970, was 16.2mm.

So why would someone mint a coin that size? So they have a coin of the value they want, in the metal they want.

you mean 12 mm in diameter, right?