Sure. Mozart had unusual skill, but it was mainly due to piano practice. (Don't know much about Bach's backstory, so I won't comment on him)

Actually, this is an interesting point. I am also a great piano player. Many people chock this up to innate skill, when they hear me as an adult.

It's not. I just worked insanely hard at piano practice. In fact, I was a well below average piano student. My teachers were often frustrated with me, and other students were much better. However, those students are now much worse than I am. It's because in high school and middle school, I spent hours upon hours at the piano, and now I can play better.

For example, I can play very well by ear, and pump out a piece without much practice now. People think this is due to some innate talent. People ask if I have perfect pitch, was a musical prodigy, etc. I was not a prodigy, and I do not have perfect pitch (in fact I often failed the aural portion of my piano exams). What I do have is an absolutely insane number of hours that I practiced, publicly and privately, to make up for what I perceived as a deficiency.

I do not believe in innate intelligence, at least not in the general case. I believe in exceptional circumstances. For example, Mozart started playing very young and was in a very musical family. In retrospect, had my parents been more musical, I think I would have been 'better' at the piano early on, because several discoveries about music I made later on would have been inculcated in me earlier.

So in general, I reject the idea of 'innate' ability. Those that have 'innate' ability often only appear to have it. In reality, they worked insanely hard.