Not at all. I'm referring to both the stakes for individual rolls and for challenges overall.
Some systems present some mechanics that necessarily have certain stakes attached - like anything that does damage can kill you if you're 1hp away from death at the time. You could make your dungeons into padded cells where no one can get hurt, thus never invoke a mechanic that puts death even theoretically in some tail instance, on the table.
I wouldn't try it if I were claiming to run D&D, though.
I think this is irrelevant. If you don't want death as a possibility, just take it off the table up front. There are other possible outcomes to losing a combat challenge.
Remember, a freak character death is a possible outcome of /winning/ a combat challenge, too. So if you set the stakes - win the fight, gain some treasure; lose the fight be taken prisoner - the party could win or lose, with those outcomes. The four out of five of them not killed by a freak damage spike, that is. Or you could fudge the freak damage spike and return to the intended stakes.
It might be implausible to others that only certain deaths are possible and others ("ridiculous" ones) are not. I'm less concerned about implausibility, which is a matter of preference, than I am of where the technical problem is occurring such that fudging is seen as the solution.
Technical problems occur in the stats given to potential foes, the combat rules, the resolution mechanics, and the class designs, among others. It's a very complex system with many potential points of failure.
Again, if you don't want death as a possibility, change the stakes.
Meh, you could decide the 3.0 orcs in question want to take the party prisoner, even the elves, and arm them with saps to that end, instead of their customary greataxes, I suppose. I question whether it'd go over well, especially as a matter of course. But you didn't have had to go to that extreme in 4e, nor should you often need to in a 3rd+ level 5e game - you could have relatively easy fights without a meaningful risk of unintended/lame freak character deaths or other oddities. Of course, you might, conversely, have issues with 'deadly' encounters not exactly living up to the label, either, even when you mean for them to...
...and, you could always adjust that from behind the screen, too.
To have a discussion about whether fudging is a viable solution to a particular problem, I would need to have a concrete definition of what you mean by "immersion."
What I mean by "immersion" is "bizarre, nearly-impossible-to-articulate, problem some players have with some mechanics and events in-game, but not others, without being able to satisfactorily explain the distinction that makes one set intolerably immersion-shattering and the other just fine." And, yeah, that can leave you needing to make ad-hoc adjustments after the panacea 'stake setting' portion of the challenge.
I have to admit, though, you have hit on a completely effective answer to the OP's question: just never present the party with challenges that include potentially deadly dangers.