My opinion on the matter lives
over here, but I'm curious how the rest of you guys do it. When a PC fails that last saving throw, how do you handle it? Does the player get a say in their resurrection? Do you go strictly by the book? House rule it? How do you like to handle resurrection at your table?
the means and mechanics and expectations of post-death are a key element of the setting and are majorly world defining, so i have to say it varies per campaign.
i emphasize the pre-death parts a lot more - specifically i let my players know up-front that "dice will not kill your character. Your character may die from intention or from neglect but there will not be killed due to random events." So they know that barring them placing themselves intentionally into a "death obvious" circumstance or ignored by the other PCs while death approaches - then they will not die.
As for post-death, i have done many many things in campaigns over the years.
One of my most recent fantasy games, i gave each dead guy an after-death scene/vision which lead to an option to come back or not with tasks if they come back. I also added in cults to the goddess of death who believed that being brought back was a blessing from the goddess or an affront to the goddess (depending on which sect) and so either treated you as a holy figure or an abomination to be wiped out. Also provided a form of "sub-class" that only post-dead folks could access giving access to a variety of necromantic senses and such even if not spell caster. (Think prestige class with a "once dead" requirement.)
Another option i use now in a campaign is the "pre-component" concept of "soul catcher."
A soul-cather is an expensive talisman attuned to you (takes up attuned slot) which will capture and hold your soul upon death. Cheap ones hold the soul long enough for a raise dead 10 day limit or whatever while more powerful ones cost more but last until resurrection. getting raise cast is relatively speaking cheap if you can find the caster and it consumes the soul catcher. getting resurrection is very expensive since it creates a new body. Again soulcatcher is consumed. (Obviously this can translate into scifi easy - see Altered Carbon series.)
The soulcatcher model establishes a way to have the elite able to buy their death safety and not leave the general populous able to all be rezz if a nice caster decides to do so.
of course, losing your soulcatcher can have issues.
obviously, "who can make soulcatchers" is a big thing to for campaign definition.
Soul-catchers can be given as rewards for (or even enticements to take on) adventures in the service of powerful figures.
But the role of life-death-after should be a major defining element to the campaign and IMO it does not deserve a general "gaming" answer. but rather a setting specific one while i do think "pre-death" (as in "how and what can you die from" as i describe above) is exactly where that "gamey" type of decision
should be made.
That is why i like the 5e death saves... and why i used something similar though not as defined in other games - interpreting "dead" as "dying" and requiring extra and specific actions to move from the one to the other and such making "dying" a drama challenge/moment for the others.