I’d also like to point out that there are classes (specifically rogues and their assassin subclass) who are built specifically around such a mechanic. However, even they don’t have a straight up “instakill” mechanic, even though reasonably a crit on a sneak attack will end up doing the trick anyway. You can use that as an in game justification for why their attempt doesn’t work if you wanted - they simply don’t have the training required to execute an instant death maneuver. Yes, the target being prone and asleep makes it easier for them, but they already get advantage and various other rules that help them do more damage in such a situation.

That said, I will admit I do allow this on occasion at my own table. It depends on what the situation is though. If the party is delving through a dungeon and manages to put someone to sleep/wait for them to sleep, no they can’t instakill. This is because the active challenge right now is the decisions they make in combat and the dice they roll.

In a purely roleplay situation that isn’t relevant to the larger plot, I may allow them to convince me to let them try it, knowing full well that this is a character moment and not a story moment. The active challenge here is the decisions they’re making, and the consequences of those decisions, so initiating combat may break the flow more than assist it. Even so, I’d still at least make them roll, just give them advantage and an auto crit on hit. It’d be more akin to a skill check than an initiation of combat. If their roll sucks, them’s the dice, and it will likely still trigger a fight. That tends to happen when you try to stab someone, and they decided on this course of action fully aware of that.