I'm one of these tough RPers. My character, Jericho Krios is a Nord that fights the Imperial and the Dragons. He wants Skyrim to return back to normal. I could write up a whole book about him now, but I won't, as I just have a question. Well, he joined the Academy mostly to meditate together with the magic. He's a guy that tries to find himself and his meaning, he tries to find what's powerful and what he needs. Not a very detailed description, I know.
So yeah, he became a student, found an artifact, Odmund became his personal assistant, fought the baddies ect. And now, he's the leader of the Academy. So? How can it help him?
It was never his goal to became a leader. But as he gained power now, he's trying to make it useful. But how?

I would plan expeditions for those who would like to participate, perhaps to seek out new knowledge or simply to test and grow in your own understanding in live experiments.
Many there are content to be left to their own paths it seems, so leave them to it!

Just roleplay that you turned down the title of Arch Mage and gave it to Tolfdir (something that bethesda should have had the brains to code into the game to begin with). It's severitating that you MUST become Arch Mage of the guild by doing the guild quests. Not everyone would want to be the leader.

Yea like one of the previous post, plan out expeditions into dwarven ruins with one of the apprentices since you can get them to follow you, say its for research purposes and to try figuring out what happened to them, also for the magical items i.e soul gems.

"I know you've only been in Skyrim for a couple weeks and I've known youfor one of those, but I would like you to lead this entire organization!"