The 4e fighter itself effectively "suppresses" any style of play that does not involve use-limited powers that you have to know to be able to attempt (i.e. basically everything that you ever did with any other D&D fighter). There is virtually no action that a 4e fighter could attempt that any other one could not; the powers simply codify what you can and cannot do; mostly in the form of imposing limitations that preiously didn't exist. Removing that particular mechanical structure and replacing it with something that doesn't have those limitations is the precise opposite of suppression (liberation?). That's what will get 5e to a broader audience.
Moreover, 3e had the TOB, which had some things similar to powers. The key differences however, were that it was not in the core rules, it was not called "fighter" and did not replace the core class, and was optional. The same thing, except without being forced down anyone's throat. I certainly expect the 5e rules to have a similar approach, except without waiting as long. Maybe 5e will do a monk with use-limited quasi-superpowers, or maybe they will simply release a set of rules that imposes those limitations for everyone. Optionally. (And hopefully not under the misnomer of "tactical combat").
The 3e fighter wasn't broken, didn't unbalance the game, grind it to a halt, or render it unplayable. Quite the contrary. It was part of a better-balanced, more smoothly running iteration of D&D than had previously or subsequently been accomplished. Why then, is your preference so much more important than others?
(The other editions aren't that bad either).
Well, there's sales and then there's the opinions of the fans. 4e sales (particularly the initial sales when people didn't know what they were getting) are hardly a statement of support of the fighter or any other element; while the conscientous choice to doff it and buy a 3.5 revision is pretty clearly an indictment of it. Nor do sales perfectly reflect the player base. As they say, no one takes your books away. 4e was almost certainly never the majority of D&D games, and I doubt it was ever even the plurality. 3e may not even have been the majority in its best days; though this is far more likely. There are a significant number of players still playing every edition, even the ones that aren't available for free online and still being revised (notice how WotC hates copyright violations now; it's because they're afraid of the competition-with themselves). The broader community of related games without D&D on the cover further complicates the issue.
WotC has access to the sales and poll data and playtest responses that we don't (the sort of data they collected very little of and reportedly ignored with 4e), and they've pretty much done a 180 on the fighter and the power system. Despite the fact that many of them bet their careers on those things in the past. What does that tell you? If by appeal to popularity you mean finally giving the fans what you want, WotC and me are both guilty as charged. Not that it makes sense to apply logical fallacies to game design (where popular opinion is pretty much inherently right).
Psionics = optional. Powers = not optional (because they are the foundation of the system). Big difference.
I'm sorry I can't XP you but well said!