Diablo II had "softcore" and "hardcore" modes, and I must say I find the term "permadeath" much clearer than "hardcore mode". It's been coined for roguelikes, and the term is pretty old, also well known.
I'm not sure how many RPGs have permadeath, some have "failed resurection" or such, which also kills a character permanently. "The Bards Tale" (Atari ST version) had a temple where you could bring dead characters to, and the priests tried to revive them for a good amount of gold. The attempt failed at times, and then the chracter was permanently dead. So even there "permadeath" made sense, and distinguished the final end of a character from the normal game "death".
If it is seen as an important feature sure depends on the player. I played Diablo II both in hardcore and softcore modes and it didn't make that much difference to me, but eventually I preferred softcore mode. Depending on my mood and how much I feel attached to a character, I also back up my roguelike save games (if a game allows that), so I can cheat "permadeath" in roguelikes.
To me the term is alright, describes the feature correctly, is also well known, and IMO it should be a players choice if they want to play this way or not. But I've got used to that roguelikes see it as an important feature, and that having it as default sets roguelikes somehwat apart from other RPGs. (But IMO there are other features which contribute more to the roguelike feeling of game than permadeath.)