Rules-lawyering drama queen but not a munchkin
Yes, that is the good thing about having these kinds of conversations. I started writing pretty convinced I knew what the issue was, but after some exchanges in post, feedback from fellow forum-dwellers about consequences of the proposed changes and also suggestions on how I might do things differently, the real matter becomes more evident.
The players (at least the majority of them) are actually nice in regards to the others. They do seem to abhor "wasting" actions stabilizing or healing comrades, but usually don't think twice before throwing themselves on harm's way to protect their allies or any NPC they care about. They also seem to get too stingy regarding using resources in a significant manner to make healing effective, even when, by the end of the day, they still have a lot of resources remaining. They do not shy out of burning resources to do pornographic amounts of damage, though....
It does get annoying when they are deep into the sixth or seventh encounter in the day (pretty much getting to the end of the dungeon already) and by the last rounds of combat the "bouncing" starts. And then, when combat ends, I get some players complaining about just that, which I do understand, the narrative gets really weird when this happens, and the scene as a whole is ugly. But on the other hand, I point out they managed to finish the day with significant resources unspent but still they gave themselves the luxury of being careless about healing or otherwise preventing damage or using defensive tactics. And then, sometimes, some PC dies, and everybody is not happy about that.
I know I have been playing way longer and way more often than most of my players, and I am starting to realize that maybe I should just soften the game. But then again I get second thoughts about that, as I already feel my game is not really very challenging (even though they keep on dying stupidly) and to lower the bar could lead to a game without that tension that makes the combats interesting. Do you get what I mean?
On the other hand, I could just assume their tactics as they are, and throw in encounters accordingly. I am not sure how to achieve that, though. I mean, what exactly should I adjust in the encounters to take into account that the party in general refuses to back down to defend or heal, even though they have invested classes, levels, spell selection, etc., to have all the resources for that?
I am not really looking at a rule change, just some way to solve those table issues. If changing some rule could help, good, but any other solution is as welcome. Sometimes they get too focused on killing enemies instead of understanding what is really going on in the fight. They take for granted that the best defense is a strong offense. When this is the case, the battles run really well, but when this is not the case, then bad things happen, and it is not because the game difficulty has changed, but because the challenge is different.
A little bit off-topic, but still somewhat related, this eagerness to go full offense also has other consequences. For instance, some of the players specialize in nova-alpha attacks. Sometimes it happens that they discharge such a huge amount of damage in round 1 that the enemies, without knowing what will come next, simply flee, or start using skirmish tactics, which the group hates to handle. It is funny for me because they really like to kill all opposition, to be sure not to need to handle it again later, but more often than not they fail to reach this objective just because of this tactic, and sometimes they even lose very important objectives because of that too, as the enemy doesn't even bother to keep on an already lost battle and escapes with some important item/info/MacGuffin. They point out that they understand the enemy is just reacting to their chosen approach, but nonetheless complain that this converts fights into desperate chases. Then I get puzzled that they know the cause of their problem but they can't help themselves just doing that again on the next opportunity.
This is one problem, yes. They should be dying when they do stupid things themselves, but as a team game, they more often die because somebody else neglected them, which is sad and does not always "taste well" after the game. The other problem is narrative. All this bouncing does not make for good fighting scenes.
This is the tricky part. It is not always easy to acuse someone of being selfish, as they present different behavior depending on different scenarios, and quite often they act heroically and selflessly. To me, it seems more like they are reckless, they sometimes just take the mechanics of the game regarding healing and stabilization and the "offense is the best defense" motto for granted, and get blindsided by different reactions from the enemies, or by the occasional string of bad luck in situations where luck should not have taken a part to begin with.
I still think that your problems would be fixed if you had a group of enemies that healed to full whenever a PC drops, then on the second time they regain all their resources and on a third time their downed allies likewise heal to full and get all their resources.
Or buff healing, as long as it is used on conscious targets. And have all healing on unconscious targets to always default to 1 HP.