It's a pretty big oversimplification that ignores other factors that contribute to tension. You can still build long-term tension with recharging health through things like forcing ammo and weapon management, something Halo (CE in particular) does well. Like most things of the "this killed shooters forever!!!" variety that people attribute to Halo, bad design surrounding the element in question is the real problem. I generally prefer the hybrid system of CE and Reach because you do have to be a little more careful and you get a little bit more of that tension, but the recharge dynamic works in Halo PvE because the Elites operate on the same rules, more or less, as the player. The "hide and seek" playstyle that people love to hate just doesn't apply to them, since you're forced to finish what you've started or start from square one with less ammo. You can't really say the same for a modern military shooter.
It is definitely a different story for multiplayer. Being able to reset your health automagically between kills is a big plus, otherwise you could presumably end up in situation where two players at equal skill level can just trade kills back and forth since one spawns with a higher health pool than how he left the other player.
Jonathan Blow has made an interesting game, but he ignores things that don't fit his argument sometimes. It's hard to look past the attitude.
