Right option is just more fun 90% of the time and the game is about having fun so easy choice.
Fun fact: there's no rule that you don't get a turn while dead. Granted, you're usually unconscious, but if you die from massive damage or from failing a save against an instant death affect you never go unconscious.
I love overly pedantic interpretations of the rules. It does say that participants in a battle take turns in combat. I wonder if that's enough to define that dead creatures can't act.
I believe dead creatures are objects rather than creatures but the problem is that the combat section is written in second person so it doesn't seem to matter if you're a creature or not. It simply says you take your turn.
Why would I leave the battle just because I'm dead? I can still act.
There's nothing actually saying that creatures become objects when they die. The closest is that it defines an object as "a discrete, inanimate item like a window, door, sword, book, table, chair, or stone, not a building or a vehicle that is composed of many other objects." But then you end up with circular logic. A corpse is an object because it's inanimate, it's inanimate because it can't take actions, and it can't take actions because it's an object. There is also notably nothing actually saying it's a dichotomy and that something can't be both a creature and an object. Though that does make it hard to tell which rule is more specific.
Speaking of which, there's more fun you can do with that rule. Rule Zero says that whatever the DM says goes, but that's the most general rule in the game, and therefore any rule that's more specific takes priority. That won't stop your DM from doing anything not expressly forbidden, like dropping rocks and killing the party, but it does mean they have to allow whatever crazy interaction you came up with.
Except that the rule that the more specific rule overrides the more general rule itself doesn't really work. If rule 1 says A and rule 2 says not A, you have a contradiction. One rule says A and another says not A. If rule 3 says the more specific rule applies (say that's rule 2), now you have rule 1 saying A and rules 2 and 3 saying not A, but it's still a contradiction.
