I think the sprint argument is rather interesting. I strongly dislike the mechanic as it's been implemented in Halo as of late, all it does is slow the game down - forcing you to pull your weapon up and slow down before firing. Let's not beat around the bush, Halo's sprint wasn't implemented because the developers of Reach, 4 or 5 had interesting ideas for it, or genuinely believed in the mechanic bettering Halo - no, it was implemented because every other shooter had it. That doesn't mean it has to be terrible, though, and it makes me think back to a similar arena shooter's implementation of sprint; that being Half-Life 2 and it's sprint mechanics. In Half-Life 2, you have three speeds: walking, running and sprinting. Walking and running are only a smidge slower than their Half-Life 1 counterparts, while running is significantly faster, all the while all sprinting does is just that it makes you run faster. You can still shoot, duck and jump the same as you would running, just you're movement speed is faster, so Half-Life 2 isn't retroactively slowing itself down because of the mechanic, rather it's making you think about combat encounters more carefully if you want to keep your momentum going.
Now how does this apply to Halo? Well in terms of multiplayer, it doesn't. In fact even for campaign you shouldn't copy Valve's homework, it's more-so an example of a game that creatively included the mechanic without copying the CoD template. For multiplayer, sprint does not belong in Halo, period. You either have a Reach situation where your maps aren't designed around everyone sprinting, so people get through set pieces way too quickly and frustrates players without sprint, and players who use it feel confined to such small spaces - then you have the opposite problem with a game designed around sprint, the levels feel needlessly stretched out, where the purpose of sprint is meaningless because you're traversing these larger maps the same equivalent speed as you would the classic maps. That argument is tired and has been done to death, though. Where I think sprint does have a place is in the campaign, so long as you don't design around it. If I were asked to implement sprint in a Halo game, I would have it enabled through a skull. No score multipliers, similar to the purely beneficial skulls in CEA and H2A. You enable the skull, and instead of a flashlight once you push the flashlight key (wherever you decide to bind it) you start sprinting, not in a CoD-like fashion however, instead you start running significantly faster than your base run, all the while maintaining all previous abilities: such as shooting and the like. You have a short period of stamina, if you exhaust all your sprint, you must wait for it to completely recharge before you can sprint again.
Okay, that is a lot of effort put towards a skull, but it's one of the only ways I could see such a mechanic working. You can't make it an option always available because that would force the speedrunning community to conform to sprint, plus it'd be way too tempting to start designing sections around sprint. At the same time a lot of people would love the option, hell I, (a classic Halo fan with zero interest in sprint or any of the advanced mobility) would definitely use it to bypass some more lengthy, less replayable sections. In addition, it'd give you a custom games option, so you could have a classic Halo multiplayer across the board, with options to accommodate modern Halo fans in custom games. Everybody wins! ...Sorta. I'm fully aware that having a few custom games options won't satisfy the tastes of many modern Halo fans, and really truly it isn't fair. Infinite won't be fair to one of the spit sides in the community, and honestly odds are they'll favor the modern fans. In my hypothetical Halo title it'd probably be the reverse, mainly because that's what well... what I would play. If Infinite plays like Halo 5 again, I probably won't play it's multiplayer. I'll run through it's campaign and be done-so, because I don't find advanced movement fun. And that's precisely what I tried accommodating here with this sprint concept, something that isn't necessary, nor is gamebreaking for classic fans - but maybe some fun little extra movement options for modern fans.