And that one's a two way thing. You don't need one or the other to be good or great or what have you. Of course it won't hurt to know as much as you can, but the top priority of things to learn should be what you want to learn. What you feel will make you the player that you want to be. Not what will necessarily make you good or great, but what will allow you to create music that you want to create. Yngwie is known for his metal and classical influence and it shows so clear in his sound that you'd have to be deaf not to notice. However he's not known for his country influence. Namely because he doesn't have much, if any, country influence. And while it probably wouldn't hurt his variety to put something as abstract as country in the he's shown little desire to create music of such a nature and there for has stuck with what he wants to play. And he plays what he plays well enough to be reputated as one of the best at it. On the other hand, case in note, Yngwie's variety suffers and a lot of his stuff sounds the same and he could also use a little bit of diversity. So it really goes both ways and your best bet is to just learn what you want and if that involves being rounded then cheers, if not then more power to you.

Edit note: My disagreement with the above statement is in the taking lessons from a teacher deal. While I'll agree that a teacher can help, I don't agree that it's as mandatory as you imply. Plenty of the greats are completely self taught. Joe Satriani is one of them and not only did he just excel to being referred to as one of the best, he also taught plenty of people who are also considered some of the best now. Not that I completely disagree with teachers, just that I think that you can learn for yourself through good reading, observing others, and communicating with others. Which are all reasons why I am where I am. Not trying to blow my own horn, just saying that I'm decent for what I am and I've gotten this way because I've done a lot of reading on the subject and when I came across something I didn't understand I'd ask someone and/or watch a video displaying what I wasn't understanding.