I'd like it if skills and class abilities would have a clean cut:
Class abilities is something unique to the class with the ability and something every member of that class has.
Skills are something that are purely optional (not as a system but you don't have to get any one specific skill for your character to work) and work mostly the same for all classes.
3.5 made such a change already when they got away with animal empathy as a skill and made it (or rather wild empathy) a class ability for druids and rangers. (By the way, I like the Book of Experimental Might's implementation: You get to use diplomacy on animals)
Some of the changes that would follow from implementing this philosophy would be:
Attempting to write a spell into your spellbook would no longer require a spellcraft check. Instead, it would be a caster level check or something like this for wizards.
Search/Perception would enable everyone to search for traps period. Change trapfinding so that you get an automatic check, just like elves and secret doors.
Everyone with survival can track.
Bards' abilities are a tough one. Everyone should be able to sing, dance, play an instrument and so on, but I like bards' abilities being tied to performance. Could be the exception that proves the rule. But the minimum ranks in perform you need to use the abilities should go (regardless of whether skill points stay in or not). Maybe tie them to a check or something.
That way, no one would be forced to take any one skill for his character to work just because of his class, and it would be a clean distinction.