Let me try this another way.
This was absolutely a Dungeons & Dragons game. No question about it, even for those who argue in the manner that you describe. We know who they are, and why we reserve a grain of salt for everything they say after. It is, in fact, my favorite expression of that game to date.
But would it have done better if it were "D&D the Adventure Game" instead of "D&D the Roleplaying Game (version 4.x)"? Plain and simple, I think it would've been better if it wasn't "Fourth Edition" of a game that had a lot of baked-in expectations and prerequisites to be called the next iteration of said "roleplaying game, known as Dungeons & Dragons".
And I am 100% convinced it would have died in obscurity, with 95% or more of D&D players never even looking at it, let alone playing it. Putting it in that position would guaranteed kill it off dead, even before you consider that being "D&D the Adventure Game" would have meant it got zip-zero-zilch-nada additional support after publication.
I mean, as it stands, at least half the people who criticized it never played or even read it either, given the pernicious and dead-wrong "criticisms" that were the stock and trade of the edition war (and thus still linger with us today).
Also? I'm
certain you did not mean it, but...well, there's really no other way to read your distinction there as anything other than "4e isn't for roleplaying." Which is both untrue and deeply, deeply frustrating, because that, too, is a longstanding insult without any basis, other than efforts to exclude 4e from being "true" D&D.
Clearly, there is room now for alternate expressions of D&D now that we have everything from cookbooks, to themes of other popular board games, to unique board and card games, and meat sticks!
PF2e says otherwise. It might not have been an outright failure, but it objectively failed to hold any of the market-share gains that PF1e had made. PF2e was 1.4% of all campaigns run on Roll20 in the last report I have access to (Q3 2021), and no report from the time PF2e was published shows it ever achieving more than a roughly equivalent amount (~1.6% is the highest I've been able to find; unfortunately, some of the Orr Reports are lost to time now.)
And the reason is very simple. It, like 4e, said "Sorry guys, the 3e engine is just
really really broken, we've tried all we could to fix it, it just isn't fixable. We have to replace things. Please give us a chance to show what we can do." (Of course, Jason Bulmahn was much more articulate and persuasive, but that's the high-level summary of his argument.) Fans of 3e don't want to be told about the ways that it
really truly does have serious, fundamental, systemic issues. They don't want to be told that the system they had legitimate fun with, that they enjoyed and found awe-inspiring and refreshing and immersive and all the other things--all responses that are
perfectly valid--is a system that the designers have run into a dead end with and can't keep going. They want that system to remain unchanged forever, except for the few,
exceedingly rare exceptions where they'll deign to grant any criticism at all--Advantage/Disadvantage being the primary example.
It has nothing to do with "dissociated mechanics", or whether the game is "adventure" vs "roleplay", or Fighters turning into wizards and shooting lightning out of their butts. It has everything to do with folks having real, legitimate, perfectly valid joy that they derived from 3e...and thus taking any criticism thereof as a criticism of their joy, their experience, and (in at least some cases) their
identity.