Are hit points outdated? Hit points get a lot of discussion in D&D circles. They're an iconic part of the game, and, like all iconography, they are often targeted by iconoclasts. Still, they remain part of the bedrock of D&D - though not of gaming in general. For me, they work, in all their abstract yet satisfying glory. They don't work for everyone, though, and what they represent is the core issue of virtually all arguments about them.
Some arguments take the tack that in a world where dragons and spellcasters exist, the very concept of hit points is, essentially, just as hand-wavey as Wish spells. But D&D's baseline humans are no more magical than in movies and tv. I mean the bystanders, the workers that exude boredom when being quizzed by detectives in Law and Order, and the corpses that kick off the L&O investigation. Not the most durable folk. Not much magic there. Four hit points doesn't go far.
Hit points reflect much more than sheer physicality. Fate, destiny, luck, muscle memory, instinct, training, all of these things figure in to the concept of hit points. All those last second dodges and hails of bullets that strike everywhere but miss the protagonist are expressions of hit points (yeah, and Armor Class, too, but that's for another post).
The Commoner in the 5e Monster Manual, or the 0-level NPC of the early days of AD&D, is the normal human, with 3 or 4 hit points. D&D PCs are the action heroes of the game, akin to Schwarzenegger or Bruce Lee. It's not necessarily magic, but, rather, action movie logic. Which I suppose is a kind of non-magical magic.
One obstacle that gets in the way of hit point critics enjoying them is the supposed lack of the "instakill," the stealthy strike, the single devastating blow that takes out a target. Especially if that target is a Big Bad. Look, instakills are built into the system; low-hit-point creatures can be dispatched with a sword thrust or a dagger slit. Higher hit points means any number of things prevent such "coup de grace"s and the like. The mind-dominated noble is jostled so his self-imposed dagger strike goes awry; the bound captive twists at the right moment; the executioner is distracted; the barbarian dodges aside of the battle axe that almost split his skull to the sternum. We've seen it in movies and shows countless times. The protagonists, antagonists, and certain important supporting characters, cheat death in amazing ways time after time.
The main problem I have with some anti-hit point arguments is the notion of something being narratively appropriate. Games are not novels, tv shows, or movies. Chance plays into the proceedings.
If you want to eliminate chance, or only allow it in certain situations, then admit it, to yourself if nobody else, and go into pure collaborative storytelling. That's not me being dismissive; there are more games than ever that focus on group tale creation. Dispense with the pretense of wanting to play a game where randomness plays a role. There's nothing wrong with that. If certain actions have to succeed due to them advancing the story, then it's more a tale than a game. When it's a game that has major mechanical elements predicated on random chance, a good DM and players know how to roll with it when that "coup de grace" doesn't work. I dare say that such things actually add to the "narrative," or the game experience, as everyone has to act and react to something they couldn't count on happening.
So I'd say it's less a matter of hit points being outdated than players and DMs who are too inflexible, or who want to simply tell a story amongst themselves.