Not sure I find this theoretical approach very helpful.
I was presenting it as theoretical because I wanted to avoid making an argument from anecdote. I run my game with wandering monsters, but it’s not random fights.
If my heroes are in the middle of healing up from low health, and I spring a wandering monster on them, they will most likely defeat it. What they will then do is get back to healing up hp. The only practical result is that story progress is delayed (assuming the wandering monsters doesn't come at such a rapid rate they deplete hp quicker than Medicine can replenish it, which I take we agree is a very safe assumption - the dungeon where the wandering monsters are deadlier than the actual dungeon doesn't seem like a fun experience, and I have never seen one in any official Paizo product anyway)
The way you make wandering monsters interesting is you add them to the dungeon’s ecology. If the players decide to spend some time healing, don’t just spring a fight on them randomly. They’ll see what you’re doing, and it’ll probably feel punitive to them. Instead, have the monsters reinforce or reoccupy areas that have already been explored. This provides an opportunity cost to resting without just randomly dinging them for some of the resources they’ve recovered. Like I said before, this isn’t entirely theoretical. My PCs are very worried about “losing progress” when they rest, so they rarely spend enough time to heal up fully.
To be fair, and you call this out too, wandering monsters aren’t necessarily a great fit for a pre-written adventure. They’re designed a certain way with a certain pacing. Since you clarified in your other response that you were talking about APs, I’ll grant you that here. You’d need to retool the dungeons to accommodate wandering monsters, which could potentially mess up the pacing. However, something like an
adversary roster might be a possible middle ground. Instead of keeping encounters static, you have them move and react to the PCs’ presence. You’re still not going ‘over budget’ in terms of overall quantity of encounters, but now you can’t just assume things will stay the same. Even WotC’s adventures are starting to use them (apparently
Rime of the Frost Maiden has one), so it’d be nice to see Paizo start doing likewise.
Wandering monsters work much better in a game where free healing is scarce and slow. If healing doesn't cost you anything, damage can't cause attrition. In Pathfinder 2, my impression is that attrition is caused through conditions, not hp loss.
Like I said above, if you can create an opportunity cost for resting, then healing is no longer free. Even if they use resources to do it faster, that’s resources they no longer have later. However, as I also agreed above, APs and adventures not designed with that in mind require separate consideration and possibly tweaks to make such an approach work properly. Anyway, I think that’s an interesting observation regarding conditions. What makes them different from healing? If someone is e.g., drained 2, they’re still effectively down hit points. Is it that they just can’t get them back on a reasonable timescale?