My understanding is that all they really do is make noise in an attempt to curry favor from the Emperor. Lots of politics, little magic.

Mages in Cyrodiil are all about politics. The Synod and the College of Whispers are too busy guarding secrets to bother to teach.

Skyrim was not J'zargo's first choice, but Winterhold is removed from politics, dedicated to study. This is the place for J'zargo to become great.