Yes, I'm bothered by the fact that I can join the mages and become their leader without being one myself. I guess I just won't join them then.
That's not the issue. The problem is in the fact that you, as a player,
know that your pure warrior can wander up to the College and casually become the Arch
mage with no more magical proficiency than the janitor. The game has failed to keep the player immersed in its world by failing to provide believable boundaries with logical solution (i.e. you can't lead the College of Winterhold without some magical proficiency. To circumvent this, gain some magical proficiency and you'll be promoted).
But that's a discussion for another thread.