To my personal surprise, the thing one of my players said he disliked most about 5E was the need to have X encounters a day.
That's just D&D from time immemorial (if you can't remember 1974, anyway).
5e is nice enough to share an approximate value of X (ok, and Y, short rests) at which it's nominally intended to balance.
Since Paizo is sensibly done with trying to be more D&D than D&D, PF2 needn't stay with that attrition paradigm.
Yes, but back in the 3.x days we didn't talk about long and short rests.
But, you still took them in 3.x: slept to prepare spells, took a few minutes out after every encounter to use the WoCLW. Really, no different from sleeping to memorize spells and resting (maybe even binding wounds, if your DM was nice) the balance of the turn after combat in, 1e.
Short rests are only meaningfully distinct from encounters, though, because 5e made them take an hour. And that's only a balance concern because a few classes have more significant short-rest resources than most.
Could it be that introducing those terms; formalizing the dichotomy, could be a bad thing?
No.
And, it's not a dichotomy, it's more complex than that. There are short & long rests, encounters, and there are short/long rest-recharge, at-will, and situational abilities.
5e has high-power/versatility long-rest-recharge heavy classes (the traditional full casters, plus Bard); moderate-power/versatility long-rest-recharge & strong at-will classes (the traditional half-casters, plus EK & AT), a high-power/versatility short-rest-recharge heavy class (the warlock), a high-power/no-versatility long-rest-recharge & strong at-will class (the barbarian), moderate-power/versatility short-test recharge & strong at-will (Monk, plus BM), modest-power/slight-versatility short-rest-rechage plus strong at-will(Champion), and no-recharge, fairly situational (Thief, Assassin).
Hard to believe PF2 will have a hard time competing with /that/, whatever it does - yet it not only must, it has essentially no chance.