delericho
Legend
Dark Sun is D&D.
Forgotten Realms is D&D.
Greyhawk is D&D.
Eberron is D&D.
Ravenloft is D&D.
Dragonlance is D&D.
etc.
If those all feel the same, then your GM is doing something wrong. Yet they all "feel like D&D" to some people. So I'm pretty sure that the "feel of D&D" is so entirely subjective that designing to fit it would lead to a very vague game.
While this is true, it is also true that there is a "core D&D experience" that most people playing the game would recognise as being D&D. Greyhawk, Forgotten Realms and Dragonlance all hew pretty closely to that. While Dark Sun, Spelljammer, and the like are D&D, they're also fairly obviously outliers to that common experience - deviating from that "core D&D experience" in some obvious (and, indeed, deliberate) ways.
So, yes, while there's no one, true definition of "the feel of D&D", it's fairly easy to develop a game that comes pretty close, and it would also be fairly easy to develop a game that is distinctly not D&D. The 3e designers deliberately set out to do so with their list of the "sacred cows" (whether they succeeded or not is an entirely different debate). The 4e designers just as deliberately did not place anywhere near as much importance in doing that, focussing instead on building the best game they could - 4e not only had a different list of "sacred cows", it also had a much shorter list.
So, no, I don't accept that talking about "the feel of D&D" is too vague to be useless, and neither do I accept that maintaining that feel should not be a major goal when developing a new edition of D&D.