Also, Planescape usually gave limits to how and how long outsiders could visit other planes, especially the prime. Most can't go there at all unless summoned or called. Eladrin can go, but only as long as no one finds out that they are outsiders, so they usually take background roles.

I could see an archon take a leadership role on the prime, if he found a way to stay and was really convinced to be better suited to the role than the mortals around him. Or an angel that was commanded by his diety to do so. I'd imagine that having a living representation of your god leading your nation would generate a lot of belief.