Perhaps upon completing the quest-lines for a faction or just the main quest part of Cyrodiil the player gets to pick a companion. Of course this would not be an "adoring fan" get-up; we would presumably craft something up that would show effort and not unnecessary annoyances.
I don't think free companions should be given out easily - you want to hike through the Jerall Mountains safely at level 6? Better have a purse loaded with septims and some hirable connections. Companion(s) would be a reward luxury for time spent, so I guess they'd be scripted to stick with the player's level and may be limited to just one or two.
Perhaps for a "post game/faction quest" thing, the companion npc would have their own mini-quest as a bonus backstory and journey thing to complete.
I wanted to put this in the faq post about mercenaries and companions, but I realized that it said Not Open For Discussion. It felt too early to call it a suggestion given what's far ahead to-do. If anyone has long-distant suggestions for the future, fill 'em in so I don't look all merc and companion crazy till I have some other idea to spas about.

