You can jump off the cliff and survive just fine. A dragon can bite you, critically even so that there is not question it's teeth are chomping on your head, and you can be relatively fine from it. You can be cut a hundred times by a sword and still be OK. You can simply wade into an army of orcs, and they can all hit you, and you can still be fine from it. You can trigger an acid trap and be fine (though it would have instantly killed you at lower levels). Poison? Disease? The same ones that would have killed you at first level are meaningless at high levels.
I admit that I truncated your first paragraph in my reply; that said, I still responded to most of your first paragraph's examples in the first paragraph of my reply. My statement about you not providing examples was specifically referring to your second paragraph's saying how the issue came up a lot at higher levels without mentioning specifically (or uniquely) high-level examples (hence why I said "this paragraph"). That said, I'll address the ones from your first paragraph that I did overlook.
[You can spread out to try and catch more air to slow your fall and/or land on your feet as opposed to your head.
You can twist so that the dragon bites your arm rather than your neck.
You can take a hundred flesh wounds from a sword before the combined tissue damage is enough to fell you, etc.
The acid trap thing isn't an issue - before it would have gotten you in the face, now it's just grazing you on the arm since you moved quickly enough.
Likewise, poison and disease dealt ability damage, not hit point damage,
Uh, it was a long list of things (seven of them) specifically pertaining to high level. Going back to the ones you covered in your initial response:
Why are you better able to do this at high levels, rather than low levels. Whatever stat covers your ability to know exactly how to do that, a first level character can have a higher stat in that thing than the 20th level character, and yet the first level character is certain death while the 20th level one is certain life. How does that make sense?
See below on acid trap, and it's even more absurd given I said the dragon rolled a ciritical hit so we know for sure it's the best hit the dragon can do. If HP covers your ability to dodge, it makes no sense.
Only in a Wuxia movie.
Wait, now agility is linked to hit points in this theory? So a character with a 25 dex and a character with a 3 dex both "move quickly enough" to dodge most of the acid (or the dragon's critical hit), in a way they could not "move quickly enough" at first level? The first level character with a 20 dex was unable to "move quickly enough" but the 3 dex guy at high levels could? That makes no sense.
Some deal hit point damage and, as this is a discussion of hit points, I think it's pretty obvious those are the ones I mean. So, let's talk about those.
It is interesting that older editions never had this 'damage' = physical injury meme. In fact, both first and second edition had sections that disabused one of this. Despite terms like 'damage' 'healing' & such, Hit points have always been some form of ablative script immunity that abstractions much of the details from us. It seems that it is only when designs remind us of this by playing with this abstraction that we get up in arms. Personally, I think calling them endurance points would have been a better, though not perfect, term.
I think the text tried to define HP but the rules themselves were both, a lot of both.
Incidentally, does martial 'warlord style' healing even exist in D&D Next?
Your turn comes up. You swing at the dragon and miss. Drat. Bad luck. But now you announce that you're dealing damage anyway. Uh... what? Wait, didn't you miss? How are you dealing damage? The connection between mechanics and fiction is no longer obvious and trivial. People have to stop and think about it, instead of getting on with the battle.
D&D is a wuxia/action movie - the PCs are all John McClanes. It's not supposed to be a model for realistic combat, and nobody is saying it is.
Remember, this is contrasted with the idea of an acid trap hitting you, and apparently just demoralizing you, since a warlord can then chew you out and you're back at full hit points. Which makes less sense?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.