I'm a little late getting back into this discussion, but here goes.
I agree with Favyn's overall point that the best way to innovate in Halo is through things external to the player, i.e., the sandbox and interactions with it, rather than through core player attributes like movement and default abilities. The biggest thing that frustrates me with Halo 5 is the Spartan Abilities. It fundamentally changes the pacing and flow of the game. By changing the Spartans from "walking tanks" to "fighter jets," Halo 5 abandoned the slower, more methodical pace of combat in previous games in favor of a twitchier high-mobility experience, and in doing so made Halo 5 not feel very much like a Halo game. I cannot say I'm a fan. At my age I simply have a hard time keeping up with the fast pace and maximalist design of the game in multiplayer. I'm good at classic Halo, but I can't seem to do nearly as well in Halo 5. In recent months I grew so increasingly frustrated with Halo 5's multiplayer that I stopped playing entirely, and I haven't touched it in seven weeks, though I still play the MCC regularly.
Halo Infinite really needs to go back to basics for the core player attributes. No Spartan abilities, and preferably no sprint as a default ability (and hopefully the decline of the "mobility shooter" has discouraged 343i from emulating that subgenre again). In general, if the gameplay needs to evolve it should do so in the ways Fayvn suggested: new additions to the sandbox, new interactions with them, and the like. The Campaign can evolve through level design, encounter design, and even general improvements to the AI. If the MP needs to evolve, then it ought to do so through innovations in map designs and game modes. For example, I'd like to see ideas from Invasion and Warzone expanded upon, with a dash of Battlefield added, to produce a truly massive large-scale Big Team experience that supports at minimum 16v16, if not more, with appropriately large-scale maps to go with it (as opposed to the constrained, congested maps in Warzone, which weren't any bigger than Blood Gulch in terms of playable surface area).
I wanted to talk more specifically about some other things brought up in this thread, but that'll have to wait. I have to be to work soon.