Here is where we differ. While I played 4E and for me it was "real D&D," it did have a rather different quality to it than 3E, and in that sense was
more of a departure from traditional/classic D&D (or AD&D) than 3E was from 2E, and I would say overall was, if not quite the "red-headed stepchild" of the D&D family, then certainly the black sheep. This is not meant in a pejorative manner! I, for one, love black sheep (and am a bit of one myself)!
My experience was rather similar to permerton's, except I had a very different reaction. I played 4e and enjoyed it, but I always felt, "Wow, this is quite a different kind of game from Classic D&D..." Then I saw the rules for 3e, which I'd missed, and it seemed like a mash-up of the 2e rules and 3e rules.
I've always thought that OD&D through 4e was something like a spectrum, distinct differences at certain points, but blurry transitions at others. So if you were playing OD&D, that was a relatively smooth transition to AD&D (or alternatively XD&D). But as people were moving out of "exploration/problem solving" and into "story and setting", 2nd Edition focused on that. If you were an OD&D player who used AD&D books, it was too different. But if you were an AD&D player running Dragonlance-style games, it was a smooth transition. And if you were an AD&D player who used 2nd Ed materials, 3e was a huge change, maybe changed too much. But if you had played a lot with the supplemental material (Complete Handbooks, Skills & Powers, etc), the move to 3e wasn't such a big change. And if you were a 2nd Ed player who used 3e books, 4e was this whole other thing. But if you were a 3e player who really got into the nitty-gritty of character generation and interactions with rules, the move to 4e was not much different than going from descending to ascending AC -- same idea, better presentation.
But I don't think most people who didn't like 4E didn't like it because they thought it was "poorly designed," or if they did I would suggest that they--or many of them--were projecting their feelings onto the game system itself. I think for the people who actively disliked 4E it was more of an affective, gut feeling - partially a response to WotC's early "anti-3E" campaign, partially not gelling with the mechanics, in particular AEDU, partially not liking the aesthetic of 4E and its incorporation of non-traditional elements into the core (e.g. dragonborn, eladrin, etc).
Really, the question of quality of design depends a lot on what you want out of the game. If you want to use the rules as a physics generator, 4e design sucked. If you saw the rules as abstractions on which to hang your roleplay, 4e was awesomely designed. 4e really had to be wrangled to work for classic dungeoncrawls (and produce the same kind of tension and dread), but it did set-piece battles like no one else.
On the front page of this site is a quote from Chris Perkins: "A great deal of my time and effort was spent to inject the fun that had been sucked out of D&D."
To me, that seems to carry an implication that 4e (and 3e?) sucked the fun out of D&D. That's pretty harsh! The difference in widespread public response to this, compared to the grapple video WotC produced at the time of 4e launch, is interesting, but I don't think the harshness of the criticism of the earlier edition has anything to do with it.
FWIW, Chris Perkins replied to that tweet, saying, "Out of context, this sounds bad.
" Gamehole Con replied, "Sorry, was clear in the room what you were saying, 140 characters is a bit of context killer." Asked for elaboration of context, Perkins said, "One of my goals is to make sure 5e contains lots of humor. Remember the little b&w comics in the 1e books?"
So rather than be a comment on 3e and 4e themselves, he was talking about a pan-edition phenomenon, something that goes back to 2e, if not late 1e.
That said, as someone whose favorite edition has generally been ignored, from the outside it's never looked to me like WotC was trashing other editions. I've always thought people imparted far too much malice into such comments, comments that were often intended to be self-deprecating, or in-group criticism.