So the thing about surgery is that it is not just manual dexterity. You need to have good enough manual dexterity combined with years of training to know where to cut, what not to cut, and what to do if you cut wrong.

Look up cataract surgery on YouTube. It's similar to some of the techniques used in this video. Could a watchmaker learn how to do this technical procedure? Probably. Would they know what patients to select, what medications to give for anaesthetic, what to do if they punctured the back of eye and the contents started to leak out, or how to deal with an infection afterwards? Probably not if they didn't go to medical school and do an ophthalmology residency....