Yes that's intentional.
I think Gygax even mentioned hit points are meant to model the sort of fighting you would see in a Erol Flynn movie (kids you might want to google that), where there is a lot of back and forth as the fight continues until one party lands a fatal blow (taking that last hp). So until you lose that last hit point you've not suffered any actual physical damage, besides perhaps a nick or two and some bruising, you are just running out of luck or stamina.
Of course then calling your hp restoring spell Cure Wounds, does really fit.
I think this was a bit disingenuous of Gygax, in a sense. Beyond maybe character level 3, hit points cannot reasonably be claimed to model actual body/health/injury status. Claims that it does are dubious at best.
So of course it's only modeling "action hero fighting logic."
I've said it before---hit points are a carryover from tactical military combat games, which abstractly represent a fighting unit's overall ability to remain nominally effective. Once the unit's "combat effectiveness" (i.e., hit points) drop to zero, the unit can no longer perform at even marginal effectiveness, and can no longer be considered a participating force in the battle.
Well, how do you translate that from a broad-scale military unit, with multiple interconnected components indicating "combat effectiveness" (personnel, equipment, supply chain, ammunition, leadership, weather conditions, terrain) to a single individual?
At the individual level, the measures of a unit's overall "combat effectiveness" is training + physical condition. But at a game mechanical level, the training aspect is largely abstracted outside of hit points; it's measured in terms of BAB/proficiency bonus, weapon bonuses, feat bonuses, etc.
So to really represent a D&D fight between say, an 8th level fighter with 97 hit points and a dire bear, any time the dire bear "hits" on an attack, what the GM should actually be saying happens is, "The bear swipes at you, but at the last second you roll away and swipe at its paw with your sword. You avoid getting raked for serious injury, but you lose 17 hit points."
But as we've seen time and time again on these forums, "damage on a miss" is utter and complete anathema to the "trad" contingent of D&D.
So . . . here we are 50 years later, and no one really knows what a hit point is, other than "the GM decides" as it occurs contextually for every attack.
Which honestly was one of the big reasons I switched to Savage Worlds in 2012. In Savage Worlds, once my character knows (s)he's hurt, (s)he's hurt. And yeah, the death spiral isn't fun. It isn't what as a player you'd choose. But it's consistent. And the "soak" mechanic in Savage Worlds using metacurrency at least is willing to acknowledge what D&D never has, which is that hitpoints have always had a huge "meta" aspect to them. Savage Worlds does it right, in my opinion, where the metacurrency aspect and the actual physical health aspect of the character are completely separated from each other. Resolve whatever metacurrency spend + checks up front. But once that resolves, if you're character's hurt, (s)he's hurt, and it's represented in the fiction that way.