I think it's more a case of people who want to become good at something, really good, tend to fall into obsession pretty easily. And the practice of trying to become very good is practice for obsession; whether it's running, swimming, basketball, playing music, painting, writing, etc. The mental effort we put into our hobby/art/sport is a form of obsession, that, well-watered,leads us further toward that.
Balance is key; I had a great rugby coach teach me what when I was 14, and all I wanted to be was the greatest rugby player in the world. What he taught was that becoming that shouldn't be a singular focus. Easier to hear than to 'do', especially for a teenager, but he's completely right.
But - to be really great at something, I think it does require a certain amount of obsession; every musician I know who can really (I mean, REALLY) play, focused ridiculously hard on their music for at least part of their years; exclusively focused, to the detriment of some other aspects of their lives, in most cases. The lucky ones are the ones who bounce out of that focus.