In the first case, if the PCs are high-level enough, dimension door or plane shift are probably more likely. But before that, keeping the tank alive through powerful healing tends to be a high priority in my experience. Intentional whack-a-mole healing would be impractically dangerous.
As for your closing questions, the answers are dependent on both the creature and the circumstance. But I don’t think it requires any great intelligence to finish off a foe, even if you can’t tell if they’re already dead or not.
To test that, I think about what a typical party of PCs would do if the roles were reversed. I think that, after the first battle in which a cleric keeps bringing their enemies back, they never take that chance again. But maybe my murderhobos are more murdery than others’?
I agree on the last thing you said. In a game where that were the tone set for how combat plays out, I would likely approach combat (overall) differently. I think that leads to a question of what I've seen others describe as "combat as war" versus "combat as sport."
Anecdotally, to touch upon the beginning of your statement:
IME, it's a surprise when an enemy can hit (and deal damage at all) to a high level tank. Against an enemy which is regularly doing so and dropping the tank, being in melee with said enemy is likely a bad idea.