I once even had a guy just walk out of my house in the middle of an encounter where his character dropped, because, in his mind "I wasn't going to be able to play my character for the rest of the night, so I have better things to do than sit around and watch you guys have fun".
I think you mentioned this before. If a player did this in my game, they would not be invited back. It is insanely disrespectful IMO.
I always said I was OK with death if it was obviously the player's fault. But too often, it's not.
While this
sometimes happens, more often than not what seems like dumb luck (a critical hit, for example) only led to death because the player
insisted on playing their PC as though they were invincible.
For example, in my last session a week ago, a player has the chance to have his PC disengage and reform with the rest of the party, but he insisted on attacking even though he was already injured and below half HP. He hit, but the monster survived and critted him, for instant death.
So, while some people might say, "Oh, that isn't fair, it was just bad luck." My answer: "Maybe, but what happened before that?" Odds are, the PC put themselves at risk and should have been considering other options.
That being said, sometimes it is just "dumb luck", but IME more often than not there are underlying circumstances.
Look at the classic "front-line Fighter". He believes it's his job to run into the fray, and hold the line, taking a beating so his allies don't have to. If anyone is going to be laying on the ground, taking death saves, it's him. For...doing what he's supposed to do?
Yes, that is his job, but not to the point of suicide. If he is pressed, he has to be able to fall back and have others pick up the slack. Unless you have a small party, most groups have at least two front-liners IME, and they can trade off duty if the encounter permits.
Few people have any real way to mitigate hit point loss
It isn't mitigated in that sense, it is withstood. Those PCs also tend to have the most hit points purposefully for taking that damage.
But despite that, I've never taken death off the table. I try to avoid it, as a DM, because it sucks for everyone. But I'm not sure what to replace it with. And if there is to be a penalty to a close brush with death...what the heck can it be, that doesn't seem grossly unfair at times?
My first suggestion would be a coma until they finish a long rest. You mentioned not doing time-sensitive missions, so that might work. If a long rest is too long, maybe just a short rest?
Another option is allowing them to spend HD to stay up, using their reaction maybe. But while at 0 hit points perhaps some penalty, like half speed, disadvantage on attacks, etc. How severe you want this is really up to your group and what they feel good with.