I agree that slightly faster kill times are needed. But that's not the reason for Halo's decline. It started with Reach which took things even further than Halo 3. Sure they added sprint but they made base movement even slower than Halo 3. They gave you a mini sniper in the DMR. CE lovers rejoiced at a long range utility, single shot weapon, but with high aim assist, bloom, and slow strafe and movement speeds, it basically meant people would ping each other at distance back and forth. Just try and get someone to play Hemorrhage in Reach. Then add in the shit mechanics of Jetpack and Armor Lock. Armor lock which would make you invincible to everything, Jetpack that would allow you to basically just run roughshod over the map design.
Couple all this with poor post launch support and you can see why Reach sucked. No universal ranks, just Arena which wasn't properly established. Weird ass title updates that either removed bloom, reduced it, basically split the player base with the CEA maps and game play, etc. Removed squad slayer, poor maps where most were Forge remakes. It just wasn't a good game and you finally saw Halo fans step back from the series. Whatever Halo CE fans felt about 2 and 3, they still played those games. But for once, people would rather not play Halo than play it.
And then came Halo 4. Instead of thinking they learned from Reach, they take it one step further. Adding in more armor abilities, making sprint universal, instant respawn which meant someone could die, respawn and sprint back and kill the player who killed him before his Shields even recharged, global ordnance which meant randomly weapons would be placed on match. One team can get a fuel rod Cannon near base, another could get a needler. Personal ordnance where you could have 2 snipers in play, 2 rockets, binary rifle, Spartan laser. Basically making each map a heavies. Why go and play in the map when I can camp and just get assists and call down power weapons at my feet.
The worst is perhaps load outs and perks which essentially broke the game. Close quarters combat thrown out the window by allowing people the boltshot which before nerf was basically a shotgun at all times. Perks like ammo which meant you could get like 6 incineration Cannon shots. Stealth coupled with active camo meant you could basically be invisible to players at will. Wait till sniper is available in personal ordnance, die, respawn with camo/Stealth and you are basically an invisible sniper. Plasma pistol and plasma grenade load outs also mean vehicle combat was gone as you could easily destroy anything. Oh, you sprint in, are about to die, throw a plasma as a martyr, die and then respawn and do it again etc.
Game play was no longer about skill, but random elements of luck and chance. Matches decided in menus rather than on the field.
