Does Perma Death make a game scarier?

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If you're properly immersed, you're not going to think like "Ok i can die i won't lose progress anyway "

Too me, perma death was just annoyance and frustrating. I was so immersed while playing the original that the "Its just a game, i won't lose anything if i die" never came up to my mind

Exactly the point I was trying to make. You can literally make the: "Oh there is no consequence for dying" argument for anything you can think of. Problem with that argument is that there is never any real consequence for dying in a video game. The worst that can happen is you lose time, but that is a meta-game concept that has no bearing on immersion. If you're thinking: "Fuck! I don't want to die because then all of this would be pointless and all my progress would be lost", are you really more afraid of the game itself?