Basically agreeing that no matter how crazy, stupid, or thoughtless an action a player may take... I can't kill him unless he says so.
This is a problem.. if it's a problem. It assumes
1) There is actually a player playing his character this way
2) The group or at least the DM do not like where this leads the game (bizarre world?)
In other words, it becomes a problem if the play styles between DM and player don't match. Imagine if the same player would continually play such characters in your campaign - every time he plays his character stupid and mindless, and if his PC dies, he just rolls up another character that acts the same way (or gets him raised). If you don't like it with the Death Flag, you won't like it without it.
I guess I could see this more if it applied equally to players and DM NPC's (but I'm getting the general impression this is not the case in these types of games)...then yes we are choosing to tell a collaborative story (Like tv, novels, etc.) and the main villain won't die early because you were smart or lucky or played well, he will die when I, the DM, feel it is naratively appropriate just like your PC's.
Well, as others have said, Death Flags for NPCs are a possibility. Especially if this is a house rule, you can do it how you prefer anyway, and some groups might definitely prefer to meet their arch villain multiple times (I sometimes miss this opportunity. The satisfaction of defeating a recurring villain is potentially a lot larger then just defeating the villain of the session)
I am not running any "Death Flag" games, but I always considered to use a certain meta-game mechanics to facilitate the story in certain ways. Some games allow the DM to offer "amping up" the risks (or even force it) for the PCs, but has to reward them. But if the players disagree, they might have to spend some game resources to decline this option. You could do the same in a villain encounter: "You know guys, this villain is pretty important. You get one action point, but the villain can't be killed. Don't like it? Raise your Death Flag, and the guy can be killed - just like you."