In Hong Kong, the coins have different size and shaped ridges so that people with vision impairments can more easily distinguish between them! I remember the five dollar coin being big and round, the one was round and thinner too, while the two was more bumpy. And although the paper bill for $10 is more common now, the ten dollar coin was small than the other dollars while being quite thick.

Many other countries have something similar, but I do like the HK coins personally. As a kid I always played around with them and sorting them by thickness, aligning their ridges (particularly for the $2 coin), etc.

And indeed, none are sharp for the reasons you mentioned. Most coins have ridges though, as those are used to tell if some of the coin was sanded off for the metal.