True. But anything is better than two weapon limits and regen health in a singleplayer game. Not even just FPS. A two weapon limit is far too restrictive in the case of combat freedom, strategy and management, and a 75% regen health trivializes health management. This is without getting into all the other things it removed. Halo isn't a good (singleplayer) game, sorry.
This is what I like about you, you actually argue instead of pressing buttons because somebody defended a game that is le bad.
As for your points, I can't agree. I've already argued why I think regenerating health is good previously on this site (depending on circumstance and general game design goals. also, Halo CE only had regenerating shields, health was separate and non-regenerating). As for weapons, I think if anything it adds strategy and management because you're always trading off something else. A Magnum is more ammo efficient than a rocket launcher on a per-enemy basis, but the rocket launcher is so much stronger and will help with tanky enemies or vehicles. You just don't have to think about something like this or make that tradeoff in Doom or Quake.
Bear in mind that Doom is intended to be played from a pistol start. With that maps do absolutely tend to have ammo management as a focus.
I'd agree if it wasn't for the fact you get a shotgun in E1M1 and chaingun in like E1M3, and both are pretty ammo efficient, especially the shotgun.