The problem with classes like, say, rogues in pre-4E is that their sum total of combat usefulness IS "+X damage except against blah." If we're going to continue with blanket immunities, then I would like to see a more diverse combat skill-set, NOT related to damage so that they can still contribute meaningfully in encounters where their damage tops out at 1d6+1. For instance, using attacks to expose weak points for teammates, or whatever.
On the flip-side, the fighter in every edition is just horrible in non-combat encounters. I like fighters, and I like roleplaying, and I don't like chanting the mantra "please, DM, don't look at my character sheet" in my head while I'm roleplaying. Now, out-of-combat is easier to solve, house-ruling-wise. Implementing Backgrounds from 4th Age is a great solution, but even a bit more lenience on class skills is sufficient to fix most of those problems.
The problem of combat usefulness, however, is a tougher nut to crack.