No need to apologise; thank you for taking the time to write such a detailed reply! I realise now that my comment might have come across as a bit facetious (in the sense that it can be read as "games are programmed with numbers so of course you can't take away the numbers") - that wasn't my intention!
I definitely like the suggestion to make hitpoints more meaningful and less arbitrary. Super Mario Brothers is an excellent example of that which I'd never even considered before. One other that popped into my head was 'This War of Mine' in the way that they handle sickness, injury, and depression: The game deliberately makes these ambiguous by only having vague descriptors for each 'level' of a condition (e.g. 'slightly sick', 'sick', 'severely ill') which is particularly effective because it reinforces the game's overall mood of fear and uncertainty.
The recent 'Into the Breach' has a different but still interesting approach: it does use hitpoints but they act more as a resource to be spent, using your characters to block damage which would otherwise destroy an objective, for example.
I also agree that more games should experiment with different success / failure states than the traditional win and continue / die and restart (Portal is a good example). I think Pyre has an interesting approach on that one, too - failures don't hold the player back but instead have an emotional weight to them because of how they affect the characters / story.
I don't think all genres will be able to shake them off (MOBAs and competitive FPS, for example) but maybe even they can change.