I'm not sure I understand the complaint. Action adventure spies are not meaningfully different than sword and sorcery heroes in this regard. In fiction, characters succumb to their Wounds only when dramatically appropriate. In games, they lose HP. What's the problem?
What don't you understand?
The point seems incredibly clear.
D&D doesn't have characters "only succumb to their wounds when it's dramatically appropriate". That's now how HP work at all. It can be in fact completely dramatically inappropriate, and the ever-increasing amount of HP from levels is really, really bad for this, too.
Three key tropes that no version of actual TSR/WotC D&D supports, and that, as I recall, neither Spycraft nor d20 Modern supported (correct me if I'm wrong), but which are ever-present in the spy genre, appearing in almost every spy movie:
1) Sneaking up on enemies and instantly or quickly and silently incapacitating them. This needs to even be able to happen to enemies, who, in combat, are fairly tough.
2) Picking people off with sniper rifles or the like. Again, this is basically similar 1, but implemented differently. It probably can be asymmetrical in that maybe it can't happen to PCs, but there needs to be a system where you can snipe people, but if you're in actual combat with them, they're much harder to take down.
3) Shooting a badguy in the head and killing them instantly in a situation that isn't the above, but is perhaps "holding them gunpoint". This is complicated by the fact that there needs to some potential counterplay.
4) PCs need to be possible to KO without grinding them down in the right circumstance - and again, as John pointed out, in spy media, you can be KO'd, and if you're uninjured, you come around on basically "full health", whereas if you're injured, you'll still be injured.
Infinitely increasing HP, the WotC edition approach to HP is very, very incompatible with this sort of thing. As John said, games with a small, fixed pool of HP can basically naturally handle this, or handle it with small rules additions.
With WotC HP approaches, you need multiple special subsystems to handle things like this, which again, no TSR or WotC edition has, and which d20 Modern and Spycraft didn't have IIRC (again, correct me if I'm wrong).
In fact the only d20-based RPG I'm away of which even has a subsystem anything like this is the "X Without Number" series.
Also, as an aside, D&D is pretty bad as a system for Sword and Sorcery - a bunch of S&S common tropes are not really doable in D&D - hell that's why Worlds Without Number added a bunch of subsystems, so that a D&D-ish OSR chassis could actually do more Sword and Sorcery staples.
This is the tip of the iceberg too. Skills starting extremely low and going extremely high as you level up is another huge, huge problem for this genre. A better model would be where you barely even made skill checks if it was something you were supposed to be specialized in, and instead gained "abilities" related to skills as you levelled up (i.e. a hacker might gain the ability to nigh-instantly hack a camera system).
(This avoids the question of whether level elevating hit points are a good model even for the former, but that's a separate discussion).
For Sword & Sorcery? They're not. Much higher starting HP with limited or no HP gain (perhaps only from actual choices/options) would be a much closer model for most Sword & Sorcery stuff, as would some kind of "injury test" system. BRP fantasy games are better at this than D&D is.
D&D has effectively been "grandfathered" in for Sword & Sorcery, but other genres don't have that grandfather factor.