This sounds fairly reasonable...
...until you remember 5e also shares the
exact same legacy.
Literally nothing available to the PF2 devs weren't also available to the 5e devs...
except one teensy weensy nugget of information: the knowledge designing your game like 5e brings immeasurable popularity.
Then your argument falls apart entirely - since no, there's no inevitability in "having 3.5 as common ancestor" (not to speak of your nonsense that 4e trusted the DM more than 3.5) leading to "locked down ruleset".
...and so the question remains unanswered:
What do you think are the reasons for Paizo following in the footsteps of the clearly least successful edition of D&D, even though they had a blindingly obvious model for success right in front of their eyes?
At best, your argument can make us rephrase the question to:
What did the 5E devs realize that the PF2 devs didn't?
It should also make us appreciate 5E for what it is and for what it did. Despite this doom of having 3.5 as your "common ancestor" they still managed to finally fix LFQW, all without locking down the game or infesting it with a thousand little feats.