Not having the benefit of a lot of play experience, let give a concrete example of what I'm picturing and you can tell me what's wrong with the picture. Imagine a cave complex of troglodytes. There are multiple rooms of troglodytes, most with 2-3 trogs, and some with 4-6. The party is strong enough to where 2-3 trogs is simple, 4-6 is a challenge, 7-9 is really tough, and 10+ forget about it. The trogs are somewhat organized, and may support each other in some cases, but usually it takes strong leadership to really bring them together. Furthermore, there's a little bit of movement around the complex so that every 30 minutes or so there's a 50/50 chance that a patrol of 2-3 runs into them. Patrols always either reinforce a room or bring reinforcements.
As the party explores, if they are careful they take multiple smaller rooms independently, never needing to slow down too much for healing. If they aren't careful, one of the encounters could easily ballon into a real challenge. If they slow down too much, they may get caught by a patrol and then have a real challenge. They'll quickly learn that not being careful and going too slow is a losing proposition. Eventually they'll probably decide to retreat and regroup.
If the party retreats, the trogs will discover they have been invaded and might consolidate into a strong base of 10+. What should they do? Here they can try divide and conquer tactics, or just avoid the strong base for a while until enough time has passed and the trogs decide the danger is over. Better hope the party is scouting and playing smartly.
This is exactly what you would expect, coming from anything from AD&D or 5E, or, dunno, Savage Worlds or Tunnels & Trolls.
In PF2, the game math mandates a completely different approach. See, PF2 doesn't do "2-3 trogs is simple, 4-6 is a challenge, 7-9 is really tough, and 10+ forget about it" at all.
Let's use actual Bestiary numbers to illustrate: Warriors are level 1, Skulkers level 2 and Leaders level 3. Let's furthermore assume the party consists of four level 2 heroes. (The math is exactly the same if your monsters are levels 8, 9, and 10 and you are level 9).
Then I'd say a single Warrior is what you'd call "simple."
Two Warriors or one Warrior and one Skulker is "a challenge".
Three or four Warriors, two Skulkers, or one Leader and one Warrior is "really tough".
Combine any two of the previous encounters, and you are immediately in "really tough" territory, if not outright "forget about it".
Only "simple" encounters mean there's a real chance of not taking significant damage. As soon as you face a "challenge", chances are at least one hero will lose half his hit points, and require healing.
At such a low level, Medicine will keep pace, so that the 10 minute downtime per encounter schedule might seem workable. As you level up, you realize you're more realistically looking at 20, 30 or even 40 minutes downtime per encounter on average. (So a dozen encounters takes four or six hours, 99% spent resting). You might bring this down by focusing your party's capacity for healing. On the other hand, any party without Medicine will definitely need two or more days to wrap it up.
More importantly, you hopefully see that the space for reinforcements is next to zero. You speak of a wandering patrol of three Trogs. I'm assuming Warriors. You can't add that to any challenging fight or you'd look at a possible TPK. At the very least you would turn the game into fantasy naughty word Vietnam, because of the harrowing difficulty.
So even hours after entering the Trog caves, and half a dozen rooms cleared, you have basically no room to play the Trogs smart, or you immediately overwhelm the heroes.
You can absolutely expect them to change gears, turning to guerilla-style warfare, or protacted diplomacy or whatever. Many groups don't enjoy that, though. (I should clearly state that this isn't even discussed in Paizo's APs).
What you can't do is just keep on trucking like you were playing another game. To do that you need enemies of at the very least three levels lower (preferably more).
Or, as I've stated already, you need to transform the game by losing level to proficiency, loosening up the very very tight math.
Ergo my conclusion: the game comes set for 4E-style combat set-pieces out of the box. If you want it to support sandbox play, you need to change something.