Likely not. That's already way into overthinking-it territory.
Death is a known possible outcome, just as are other Bad Things e.g. limb loss, level loss, item/wealth loss, ability loss, forced alignment change, etc. etc. That 5e has taken most of those Bad Things right off the table is what has led to the current focus on death: it's all that's left.
Also worth noting that most of those other Bad Things can be recovered from or adapted to while still playing the same character, even at low level where death would usually be permanent.
In a system like this, if death is also taken off the table what's left to present as a credible threat to either an individual PC or a group that the character - and thus player - has to take seriously and can't just shrug off? Sure, if you're into deep immersion etc. there can be serious emotional threats to the PCs, but casual players (which are, I think, the vast majority) aren't likely to care too much. They're not there for emotional angst, they're there to pull off some derring-do and laugh at the antics their characters get up to; and if some of those characters meet some Bad Things in the process, that's just part of the game.