This is indeed a fascinating subject. It sounds like Mozart, on top of his musical gifts, had an eidetic memory. Usually we associate that with visual memory, but obviously he had such a gift.

In interviews I've had discussions with several musicians about reading music. No doubt it is very useful, especially prior to audio recording such as we have today. That being acknowledged, in jazz some of the greatest musicians couldn't read music: Dave Brubeck, Chet Baker, Wes Montgomery to name a few.

In terms of the kind of ability that Mozart displayed, or musicians who seem to have extraordinary innate abilities, I wonder it there isn't something like this going on:

His innate mathematical ability, might be akin to Mozart's musical ability. Anyway, interesting to think about.