What I want is a game that, at it's core, you can pick up and play as quickly and simply as BECMI, and that's a complete game at that level if you want it to be.
But, a game that also includes customization options that can go as far as 4E's level.
And I want you to be able to play characters created both ways in the same campaign.
No, you can't make such characters 100% balanced with each other, but you can make them close enough.
Similarly, I want a D&D where you can play combat as mechanically as 4E or as abstractly as (say) 2E, and the system supported both.
I also want this from my D&D, and it seems quite plausible to me (not easy - just plausible).
Start with essentials-style characters. They generally have a mixture of class abilities, at-will and encounter powers (some of which are usable more than once/encounter) and either daily powers or static modifiers. In the customized version, the at-will and encounter powers can be swapped out for powers from a list. Similarly, packages of daily powers, class abilities and static modifiers can be swapped out for other packages, much like current classes allow players to swap out certain class abilities.
Then, as a blanket design choice, make sure that none of the default abilities depend on the battlemap in order to be effective. That way, the basic characters can either play a (less tactical) battlemap game or they can play with more abstract combat. The customizable abilities can require a map for maximal effectiveness. There is nothing stopping a player from taking a slide-style power in a map-less (or mostly map-less) game, but that's an "at your own risk" decision that depends on GM discretion to make the "slide 3" power effective in an abstract combat.
You can also simply feats and skills greatly. Skills can be replaced by ability checks, and feats can be replaced by (swap-able) non-combat class abilities.
If you use ability checks as the core mechanic, than you can just give classes bonuses to certain types of ability checks. What's the difference between training in the stealth skill and giving Rogues a +5 bonus to checks for stealth (which would typically be based on Dex) or Wizards a +5 bonus to checks involving magical knowledge or analysis (typically based on Int). Classes could also have abilities like the wilderness knack powers of Essential rangers, which could potentially be swapped for generic non-combat powers. Naturally, some of these swap-able non-combat powers would include skill-style training in certain types of ability checks.
Obviously, it's a lot easier to describe a system at a high level than it is to work out all the details, but I don't think the designers of D&D have to achieve any great breakthroughs to build such a system. It seems quite doable with "existing game design technology" (as it were).
-KS