You know what would be a great Halo game? One which goes more into the direction of Quake, Unreal Tournament and other similar games. Only to a certain extend, of course, because Halo is quite a different beast than those games. Faster movement speed, higher jumps and overall agility would be better. The person who thought sprint was a good idea would get fired. Everyone would spawn with the exact same player traits at the beginning of the match and the outcome of the match is only decided by what players do in a match. You would start with a utility weapon that's good at any range, but is outclassed by other pick-up weapons in only a certain range. More (kinds of) power-ups would be on the map. You would be able to see what kind of power-up a person has in a glance. The AR would never be a starting weapon. The amount of different gametypes would be reduced to only the ones that are actually good. You would be able to flag juggle. There would be no fall damage and no stun. You wouldn't have to play gametypes on maps for which they weren't designed. The radar would only be in Free-For-All gametypes. CQC power weapons would never be put on small maps with tight corridors. Snipers wouldn't be placed on big open maps. Vehicles would have their health tied to the driver's health. The Spartan Laser would never see daylight again. Weapons wouldn't have bloom to slow down the game to a crawl. Maps wouldn't have huge flaws in them that a monkey with no eyes riding on a bike with a hat on would notice the moment it played on the map for the first time.
It would be Halo.