To my mind, the reason why D&D originally introduced skills (somewhat reluctantly) was in reaction to the convention established by RuneQuest (and to a degree, Traveller). When they were fully integrated, many people felt a sense of vindication or relief that they had finally been made official rules.
However, on reflection, I'm just not sure that they are truly needed in the game - and certainly not as a non-optional core rule.
D&D3.0 was too fiddly with it's skill ranks that took an age to calculate, made the character sheet ugly and were over specific (Use Rope, etc). 4th edition appreciably brought the number of skills down, but my question is - what is the point of listing, say, 12 broad Skills, when you can have an even shorter list of 6 Ability scores that cover pretty much everything anyway?
People say this is an abstraction, but then so are 'skill lists' (just a more complicated abstraction!). In the real world, we don't need to list our skills in numerical form, and neither do we need to do it in our fantasy roleplaying. D&D has always been a Class and Level based system, rather than a skills based one, and it would definitely bring back a sense of identity if it celebrated this concept rather than shy away from it.
If you have a central mechanic based in some way on integrating the Class choice + Level of the character + Ability scores, (as C&C did, kinda), then this would be the real innovation for D&D. It's not realistic (but then neither are elves and dragons), but it would be fast and fun, in my view.