Why would it be parody? Where were the changes in those gameplay mechanics in the Halo series? Since 2001 we're playing pretty much the same game with updated graphics. Firing from the hip as if it's Doom...
I really wanted to like every Halo game, but as my friends said every time: "That new Halo is exactly like the last one, nothing changed"
I don't think you or your friends are invested in Halo enough to see why the games aren't really the same at all.
After CE, Halo 2 removed health and fall damage, increased melee damage, decreased grenade power, decreased fuse time on grenades, upped bullet magnetism and aim assist, switched from projectile weapons to hitscan, removed physics on power ups, added vehicle boarding, made all vehicles destructible, added a ranking system, changed movement and jump height, replaced CE Pistol with BR, added playable elites, added dual wielding, accidentally added button combos after cutting them, and featured a radically different design philosophy behind its maps (ladders/teleporters vs lifts/man cannons for example). Then there was matchmaking!
After Halo 2, Halo 3 increased melee lunge and mutual kill window, added aim acceleration, decreased grenade power, decreased grenade fuse time, decreased aim assist, switched back to projectile weapons, decreased effectiveness of dual wielding, lowered grenade limit from 8 to 4 and introduced 2 new grenades, added support weapons, added equipment, changed the ranking system, a different power weapon spawn system, redesigned objectives (assault), slowed down movement speed, made the jump floatier, decreased the field of view, redesigned some weapons (BR, Needler, Carbine, Sniper), had different elite models, removed button combos, redesigned power ups, introduced the Banshee bomb to multiplayer, introduced new vehicles such as the Hornet and Chopper, and also featured a different philosophy behind its maps (linear aggression). Then there was Theater, File Sharing and Forge.
After Halo 3, Reach reintroduced health and fall damage, brought back hitscan weapons, took away melee bleedthrough (opponents always take two melees to die regardless of prior damage so long as they had shields), introduced loadouts, made elites their own unique character model and introduced the dynamic "Invasion" game mode, removed dual wielding, increased aim assist and bullet magnetism, removed 2 grenade types, further slowed down movement and jump height, increased motion blur, nearly removed the ranking system, cooldown when dropping objectives, added armor abilities, added reticle bloom, changed radar to show player elevation, replaced BR with DMR, separated vehicle health from player health, overhauled vehicle controls such as the Banshee, replaced Hornet with Falcon, removed power ups from most maps, increased blast radius on grenades, increased hitboxes for headshots, decreased rate of fire on sniper, replaced some weapons with "older" counterparts, like Focus Rifle and Plasma Repeater, increased field of view, and most of its maps were asymmetric. And let's not forget the significant changes to Firefight or Forge.
After Reach (oh boy), Halo 4 removed health but kept fall damage, added personal ordnance drops (killstreaks), default sprint with increased duration, dumbed down the Covenant AI, introduced Promethean enemies and weapons, more armor abilities with some returning and others being replaced, decreased motion blur, added kill cams, instant respawn, custom loadouts, perks, replaced falcon with mantis, redesigned or replaced some weapons or abilities, added new grenade type, redesigned gametypes (CTF, Flood, Oddball), replaced Invasion with Dominion (domination/conquest), increased bullet magnetism and aim assist, removed the ranking system from in-game, removed camo power up and redesigned overshield, redesigned or rebalanced other weapons (beam rifle), redesigned all the audio effects, reintroduced melee bleedthrough, changed radar to show vehicles, and the maps were HUGE. Also, Spartan Ops.
Am sure there are many things I've missed (or mistaken). The point is that most of these are significant changes. The game has "evolved" every single time, and many fans would argue it's gotten worse. The one true fact is that they've never been the same, which is actually part of the problem. It's why some changes (often unnecessary ones) for the sake of "modernization" would be a mistake.
For once, I'd like to see a Halo game that doesn't fix what isn't broken or feel the need to copy everybody else. Outdated? Perhaps, but the people who didn't buy Halo because it was "the same" clearly wouldn't show up if ADS suddenly appeared. I see no reason for Halo to compromise its identity to try and win them over either.
It didn't work the last time