You know what? 343 actually gave me an idea.
Alright, so in Halo 5, while sprinting, you can hit "terminal velocity" after a bit. You can do a slide at the end.
Why not get rid of sprint, have a fast default movement speed, but when holding forward for a period of time, you naturally gain some speed until you hit "terminal velocity", or the fastest movement speed.
You can still shoot, throw grenades, and melee, and you get rid of the problem of having to walk to the battlefield in BTB, and is balanced in the fact that while in the fastest movement speed, you have to be going straight for it to work.
Well, why not?