Smart. The idea of being captured and having to escape turns the problem of failure into a puzzle rather than a twitch-based interaction. And puzzles are often a lot easier to blend with stories. But of course, puzzles come with their own issues: if it takes too long for a player to figure out how to solve the puzzle, they will be forced to "leave the story" and start focussing on the game system instead.
For example, take the novel The Road, which is far from an action packed novel, but the "action sequences" that are in it are quite important. Should this just be be skipped for games that have no failure, or is there perhaps some other way to do it?
Having never made (or even been inclined to make) an action game, I'm not the world's expert on this issue!

But I think you should only have failure as a game mechanic if failure makes sense in the narrative. The problem is that if your narrative does not involve resurrection or immortality, failure represented as death needs to be permanent.
Of course, in most stories, you don't want the protagonist to die before reaching the end of the story. So the solution is to represent failure in another way, not as death. If it's suitable for the story, perhaps you can hurt the character instead of the player. I remember feeling terrible about how my autonomous sidekick got hurt in Silent Hill 4, even if that didn't have any impact on the gameplay. Just seeing her bleeding was very painful and thus something I wanted to avoid.
This does not solve the problem of repetition, though. Repetition is not suitable for most stories. And in most games, repetition only confronts you with the systematic nature of the game. So either you figure out a way to make repetition an integral part of the experience (won't work with many stories) or you find a way to not have repetition (at the expense, possibly, of shortening the experience).
I think that there must be some kind of fear of loss and stress involved and the trick would be to do this without making the player focus on underlying mechanics.
This is easy: you just make sure that the "fear of loss and stress" come from the narrative and not from the game system. That what you lose is something you loose in the story, and not in the game-as-system. The advantage of this approach is that in most cases you won't even need character death.