That hasn't been my experience at all. I'm running the Abomination Vaults AP and it feels just like any D&D dungeon crawl adventure I've ever played in tone and story. Having played quite a bit of 5e, the adventure would work just fine being converted over. Reading ahead for the AP I'm running next (Stolen Fate), I don't get a significantly different vibe in the adventure being presented.
The AP I ran from start to finish was Extinction Curse. But I then started Abomination Vaults, and for a while it seemed like what you say. However, after the first few levels, the structure mandated by the PF2 rules reimposed itself and I burned out maybe 50-60% into the module.
The chief problem with PF2 is the same as with 4th Edition: in the long run you can't just
play D&D, you need to follow a strict rhythm of crescendo and climax (combat-wise) that can and will get in the way of role-playing.
D&D 4 should by any reasonable train of thought have taught Paizo the lesson that's not what gamers want. Paizo doing PF2 right after the crash and burn that was 4E is basically incomprehensible to me.
These games offer a solution to a problem that throws out the baby with the bathwater. Yes D&D combat can be uneven, and yes bigger set pieces can end with a whimper (or a TPK) but the solution is not to impose a structure upon play, because the exceptions (where this hinders the flow of your campaign) far outnumber the rule (where it does help you).
It's as if you want help structuring and balancing up your set pieces and end up having to make every combat such a set piece. PF2 and 4E simply... gets in the way. Far too often to be worth the benefits they bring.
Also players dislike being so controlled. Both games give off this vibe of "we don't trust you filthy minmaxers so we're going to bend backwards limiting your ability to do that" completely forgetting that player freedom during charbuild is one of the chief strengths of D&D - it's a core strength of the game that is essential to explaining why people like D&D.
PS. Paizo has already done what you suggest - there is a Abomination Vaults for 5th Edition. DS.