Actually, Mozart's training was as rigorous, or more, than anyone's nowadays. Mozart received extensive training form some of Europe's top 'educators' of the time, and he had a harsh, disciplinarian father who made sure he played his exercises!

The genius of someone like Mozart comes from retaining ones imagination and creativity AT THE SAME TIME as developing prodigious technical skills.

Some of us here I'm sure, have problems playing music he wrote before he was 10!

And yes, while there may be some trained players here that can't 'feel' their way out of a paper bag, there are probably many more untrained players that have exactly the same problem. They simply have an 'excuse'! It's no good hearing it your head if you lack the skills to do it on the keyboard, and losing the fear of taking a tune into a different key or mode is one of the ways to be a better 'instinctive' player. If your heart wants to perform a tune's bridge in F#, but your finger's can't do it, you end up following your fingers, NOT your heart.

Technique in the service of creativity and originality.... now THERE'S a thought.