And that's the fundamental issue - D&D never really tried to expand its "core". XP for non-combat situations are undefined till 3E.
My opinions on this are a little scattered, so bear with me...
I think the 'core' of D&D has been defined pretty clearly by 30 years worth of players: namely, 'killing things and taking their stuff'. No matter how the designers or individual groups might have added onto that core, it remains the common denominator. I'm all for expanding on that core, but that has to be done in light of 3 decades worth of gamers being fairly explicit about what they enjoy about D&D. And I say this as a die-hard 'corner case' DM known for combat-free sessions and generally going against the grain of whatever edition of D&D I'm running.
Also, XP 'story awards' date back to 2e. Plus, my experiences were that plenty of 1e DM's awarded XP for completing adventures/tasks, decoupling XP from pure killing.
[edit: also, part II] Another funny thing is that the move towards making all classes combat-capable happened in 3e, which greatly increased the combat effectiveness of rogues and made it far easier for casters to stand in the middle of a melee and sling spells. 4e is merely a refinement of what was began in 3e.
4E is trying to expand the non-combat part with skill challenges (that grant XP) and Quests (that grant XP).
All good ideas. Though I'm less interested in the way the rules try and incentivize non-combat activities (ie, with XP) and more concerned with how the system facilitates different characters 'getting in on the action' when they want to. One of my biggest problems with 3e is the way it rewards specialization. While I can see the reason to do this is a class-based game, its runs contrary with what I like to see at the table: namely, players trying anything and everything to overcome the challenge at hand.
... because all classes have a combat role they will fulfill well.
Really, it's about time, it's a terrific design choice. It's liberating as a DM to have all the classes competent in the game's core activity. No more worrying about spotlight time. This, coupled with inclusive bent of the skill challenge rules, and a smaller skill list with more broadly defined skills, really works with my preferred 'organic' DM'ing style. I like to let the 'plot' go wherever the players want. I dislike having to overplan/overdetermine things like encounters. I feel with 4e, whatever the actioniis, the characters stand a reasonable chance of making a meaningful contribtion, or at least, the limiting factor will be the players cleverness, and not their character class choice.
There should be more "non-combat" abilities aside from skills. Rules for covering contacts, influence, exception resources, lore, overland travel that use unique character abilities - a power system for non-combat stuff.
I'd like a book full of suggestions and advice about those things, but I have no interest in a codified rules system for them.
And of course, all those non-combat stuff needs a resolution mechanic as interesting or complex as the combat resolution mechanic. (But is that really possible? Or _really_ desirable, from a gameplay point of view...)
I have no interest in seeing those aspects of play mechanized, so from my perspective, no, it's not desirable at all.