The point is that "telling the same stories" is as useless a metric as "you could say that about Edition X".
You can pretty much take any Golarion scenario, or an old AD&D scenario, and then run that in everything from OD&D to 5th Edition.
The only thing that would constitute a hard roadblock was if the scenario depended on a particular effect that your current rules engine simply cannot reproduce. A game without scrying, teleporting or, I dunno, speaking with the dead, could not be used if the D&D adventure assumed that capability.
I mean, of course, you could still run the adventure and work around the issue, but that I consider to be something else.
Likewise, if one edition says that Umber Hulks are high level mega monsters, and another makes them fairly weak early-mid-level monsters, you might want to add or subtract a Hulk or give them Goblin allies. That too, is something else - tinkering with enemy strength is required even within the same edition just by replacing a strong party run by experienced gamers for a weaker one or one run by neophyte players.
My point here is that focusing on those metrics is unproductive. Whether a particlar dndish game is successful or not relies entirely on other factors, since it is overwhelmingly likely you can tell the same stories in game B as in game A.
Saying "we need to be able to tell the same stories" is setting the bar incredibly low. It isn't saying much, if anything at all, about the specifics of the game; the look and feel of it; the presentation, the perceived strengths and weaknesses of various classes and so on; whether the game makes you feel empowered to do what your vision of your archetype tells you you should be able to do.
In sharp contrast to the fuzzyness of that, I am postulating that if 3.0 or Pathfinder were to be issued as a new game today, five years into the reign of 5th edition, that game would crash and burn.
Why? Because of two things in particular:
1) Except at low levels, martials become glorified bodyguards for the characters with access to (high-level) magics.
2) Creating monsters in general and humanoid NPCs in particular is a nightmare at higher levels. While individual players might well like having oodles of crunch to busy themselves with, they're playing a single character each. The DM, on the other hand...
However, the game would NOT fail because
3) you can't play any given specific subclass of a previous game. Everybody accepts that not all splat content will be available right at product launch. Arguing otherwise is plain silly.
4) it doesn't feel like D&D. This game (3.0 or Pathfinder) does feel like D&D - combats can be done quick (no excess focus on battlemats or condition-tracking); different class abilities work differently mechanically; spells and magic items feel sufficiently special and magical; etc
So the question I'm asking myself is: has Paizo even tried to address issues 1 and 2?
On 2) it seems there have been progress, so that's good. Still, spells and gear loadout can still mean the effort sinks under its own weight, so I'm not exactly holding my breath..
On 1) I'm not even sure I see any "disease insight" - that Paizo is even aware the age of LFQW has passed. If they only listen to rabid PF1 fans and only look inwards, it's quite possible they think they have done enough to combat LFQW only for us to realize that Wizards (Clerics etc) can circumvent the restrictions and at high level still utterly dominate their non-magical allies. (Both PF1 and 3.5 made a lot of promises regarding fixes to 3.0 which in retrospect was utter bollocks. 5E has conclusively shown that neither game came even close to truly fixing the endemic rot inherent in the entire 3.x stock) Which, I fear, will utterly alienate their game to the masses (that have been exposed to 5th Edition).
PS. Another reason PF2 could fail would be
5) if feats doesn't come across as "helping you customizing your character", but instead come across as absolutely mandatory core building blocks of that character, with two undesirable effects:
5a) that you can't get a look and feel of your character class just by browsing that segment of the classes chapter - that core abilities are hidden away in long boring lists of feats somewhere else in the book.
5b) how this utterly betrays the promise of streamlined character creation, if players perceive looking at feat lists to be essential in building their characters. There is nothing simple and streamlined about grokking the entirety of the Playtest feat catalogs.