Death is the ultimate form of failure.
But, this isn't about failure (as you say, and I agree, "failure" can take many forms), IMO, it is about having a real risk in the game where you are possibly losing something you care* about.
Without the threat of death, the game gets ridiculous IMO and pointless because you are basically saying the PCs
can't lose! They might not win, but the game would result in a stalemate. Or, given enough "chances", they eventually will win by sheer luck alone. For instance, a high enough level PC could kill an ancient dragon with their bare hands with enough repeats.
Now, I'll freely admit I feel a bit badly (but hey, I get over it LOL!) when a PC dies just due to bad luck on a die roll. Otherwise, frankly, I have never met a DM who wasn't willing the kill the PCs... why
wouldn't you??? Boggles my mind, honestly.
(*Assuming you care about your PCs... some players don't so death isn't a threat to them.

)