Rabbitbait
Grog-nerd
Love this idea. If nothing else, I will probably go this route when I DM. Removes the metagaming from it all. Thanks!
Sure, they can, but a lot depends on the DM, etc. My question to you would be: how many of those deaths stayed dead? Part of the problem as I see it is also the ease of access to spells such as Revivify and even Raise Dead in many games, and in the presumed concept of the design of 5E that access to such powers should likely be available.
We've had many "deaths" since I've played--but as yet, short of the potential TPK I mentioned above, none of those characters have stayed dead. Most were revivified, and a couple with either raised or reincarnated. Now, as we reach higher levels, despite greater threats, those already rare deaths are becoming even rarer.
AS @Big Bucky mentions, it seems like more often than not everything will be fine, or you are facing a TPK--there seems little middle ground.
They all stayed dead. In every case the other characters have escaped but got no chance to get the body, or did not have the resources or access to get such powerful magic.