I respectfully disagree with almost everything you said. If you can teach someone art, which you can, then you can teach someone to "have talent." There are people who refuse to learn because they don't like it, or don't want to, but you can be taught just about anything.
Take Mozart from your example, he was taught to play by someone who didn't hold him back or try to stop him, that is a gift right there. What if everyone's "talent" is just being free with what you enjoy and no one is stopping you in one way or another.
Let's not even go into who decides when you have talent or not, because it's trendy and there are taste makers.