In effect, the DM is saying "death is a possibility that can arise out of some element of randomness, except when I decide otherwise." Which means, ultimately, that when your character does die, it's because the DM said so because they could just decide that didn't happen by fudging. What a terrible burden for the DM in my view!
Why not just take death off the table? Or set up some other means to resolve this (e.g. "dead" characters are actually just knocked out the scene and come back in the next scene) other than presenting it as one thing, but quietly changing it behind the scenes so it's really another? Why not just get it out in the open? What is gained?
I agree; taking your second point first; when setting up a campaign one question I always ask is "how often should we expect a character to die?" and typically I get an answer of "one or two per year of play time". I'm running Pendragon at the moment, which has a higher rate, but that is because it specifically has character death as an event that does not eliminate roleplaying.
In most games a character dying ends roleplaying opportunities. We play the game to roleplay, and you cannot roleplay a dead character in most games, so character death is essentially saying "you will no longer have any fun with this character". For some, they find that threat makes the playing of the character more fun, but I find it a tired and banal threat. If the best a GM can do to set stakes for an encounter is "if you fail your character will be taken away, then I'm honestly a little disappointed in the GM.
Pendragon has the concept of playing a family of knights though, so a character death is mitigated. You'll play the former knight's son and that character will still be a strong presence. So for Pendragon, our players are happier with increased lethality.
And that leads into your first point -- it
is too terrible a burden for the GM, and it need not be so. In most campaigns if the mechanics call for a player death, I'll ask the player how comfortable they are with that. It doesn't have to be my decision. And I have mature players who, actually, are usually fine with it. Maybe one time in five they will take my alternative out.
Like many things in GMing, talking it out upfront, and then presenting players with options to give them agency in their character's fate is just a good way to go.