Thank you for reading my thread and if you agree with it please upvote and bump it so we can increase the discussion on the boards.
As for your idea - yes. Notice that the most popular immobile champions (think Syndra, Vel'Koz) also have some kind of CC or defensive abilities, or some way to self-peel. Syndra has an unreliable stun that, if used right, can stun multiple Champions. Vel Koz has a long range 1-or-2-target slow and a fast, short range knock up that he can use to keep himself safe.
Compare this to, say, Kog'Maw, who is very immobile and has no defensive or peeling other than his crappy slow. Kog, despite his high power potential, is very unpopular because he can't complete with mobility.
To a degree this is okay for some Champions. 1 on 1, Kog'Maw can eat through tanks and has such a high late game damage output that he doesn't need to protect himself - he just eats you instead. But in a coordinated effort against a full team, he's extremely vulnerable. So he's not very often used at higher levels of play.
So an immobile champion either needs defensive/CC abilities to make up for their vulnerability, or else should have a high enough power scaling that the trade off is worth it.