I don't think we need to change Halo's movement style from the standard set by 1-3.
I disagree*. Halo stands apart because of quick decision and flexibility during battles, where tactful movement, use of surroundings, and steady aim determine winners from losers, not so much the weapon you have and if you saw someone first.
With that in mind, movement augments to the gameplay could deepen Halo's gameplay. Weapons can become more powerful as defensive options based on skillful use increase, leading to quick, skill-determinant gameplay. You can have threeshotkill weapons if you have to work to kill someone that fast.
*Well, we certainly don't need to change anything. So I disagree on principle.