What's the wizard's magic roll? Why does the cleric need to sit this one out? He can roll and look for circumstances to boost his attack roll, and being a cleric, probably has some good other stuff to do as well. What do the fighter and thief get for free due to being expert, versus what do they still roll for (special powers, special effects)?
So, you say, "Use situations where many skills can be used to the same effect."
So, how many different skills do there need to be in the game so that everyone is "sufficiently trained" in searching a room to let everyone contribute?
And keep in mind the corollary to the wizard and the cleric just sitting there: The Fighter and the Thief kill the challenger automagically, and then the battle's over.
There's no tension, no chance, no anticipation, no drama, no risk, no
game in the thing. It's all binary pass/fail (plus some DM adjudication if the players want to get creative). Which is fine for things that you just want out of the way, but lousy for things where you want some interesting interaction.
Sure, the cleric could be all, "I look for a chink in her armor!", but when the Fighter and the Thief got this handled, why would they need to?
Which is, come to think of it, some of the problem with the current 4e skill system (and skill challenges): the people with training use whatever skill they're trained in and usually pass for everyone, with a binary resolution.
If you want searching a room to be nothing more than a quick pass/fail, that's fine, and it's useful in a lot of situations.
If you want searching a room to be a chance for role-playing, exploration, drama, tension, and engagement, you're going to need more details, more options, and more chance involved. If you want searching a room to be part of the game, you have to make it something you can
play.
As a parallel, in my 4e games, I use Passive Perception to notice things that need a binary resolution: hidden things (traps, doors, and monsters), mostly. Whether the party discovers these things or not, I don't really care, and I just want a quick yes/no answer to the question of: is it seen?
However, if the room was filling up gradually with water and they were looking for the quick escape hatch, using Passive Perception would be boring. So at that point, it becomes something akin to a skill challenge. It's a BIG DEAL if they fail (they could all die!), and it's a moment of tension and drama that I want to expand out. So characters need to use their resources and abilities to overcome the challenge. This needs a different resolution system.
It's sort of the difference between an attack roll and a damage roll. If all monsters were minions, combats would be duller pass/fail tests. But most monsters have HP, which is gradually whittled away over the course of several rounds with many attempts, so drama and tension rise gradually.