They could just make you dead when your HP hit zero. How would that be?
It can certainly be a challenge, but I can't say I have so far found that it is outrageously difficult to get an unconscious player back up and into the fray.
Ideally, whether the AI does this or not should depend on the intelligence and/or behavior of the attacker. Animals tend to keep after prey until they're dead. Intelligent opponents might think it best to finish off any downed foe lest they get back into the fight (like you, me and probably everyone else would do). Or maybe they would see it best to go after the next immediate threat. Varied AI on the matter would be best.
Just making you dead when your HP hits zero wouldn't fix the problem, it would make it worse. The problem here is the AI targets KO'd characters until they are actually dead when they should stop going after the KO'd character now that they are no longer a threat, allowing the chance for them to make death saving throws and stabilize so you can help them up after the combat is over. Just straight up making them die would have the same outcome as the enemy just constantly attacking until they're dead: they don't get to make death saving throws, and your forced to revive them instead of using the help action after the fight is over. Like you said though, a varied AI system would probably be the fix to this. Almost any creature is smart enough to realize that the enemy that is currently beating them to death is more of a threat than the guy bleeding to death on the ground and not fighting back, but having some enemies just be especially sadistic like some kind of psychopath would give some variety to encounters.
The AI really needs an overhaul altogether honestly, because not only do they feel stupid they also feel super sadistic. Seriously, if the person who designed this AI was DMing my D&D session, we would be having a fight to the death in the middle of the room within an hour because they would just actively be trying to kill the PC's in the most sadistic and brutal way possible. Larian, it's not FUN for players to have to constantly revive their characters because your AI is too stupid to properly recognize threats and aggro accordingly. Plenty of RPG's out there have managed to figure out how to get their AI to aggro on certain people properly, why can't you guys? Currently having a tank in the party is completely and utterly useless because the enemies will just run right past them like they're a Wal-Mart greeter on Black Friday and the wizard in the back who hasn't even gotten his turn yet is that sweet sweet sale they're all after.
It is not fun at all to watch your enemies run right past the person meant to take the brunt of their focus and attacks, provoking numerous attacks of opportunity from your other characters while doing so, just to reach that squishy wizard in the back. It's also not fun to just get outright slaughtered by monsters that you decided to arbitrarily redesign (Looking at you Gnolls, you giggling little jerks). The logic here should be pretty simple: the wizard who hasn't had a turn yet is not as much of an obvious threat to a bunch of low intelligence monsters as the warrior who just beheaded one of their group with a giant axe. The guy unconscious on the ground is even less of a threat. So why are they targeting the characters that should be considered "low threat" right away?