Remember when Halo's innovation and ability to compete with other games was less from changing up the formula of the base game and more of adding features that were rare, especially for a console game at the time? Forge, Theater, in-game friends lists, matchmaking, new modes and gametypes, etc.
Bungie almost totally overlooked the competition when developing the Halo saga, and they mostly went straight with their own path.
This allowed Halo to be so unique and innovative in many areas (with the features you listed), but this made it also lag behind competition on other aspects (bland in-game storytelling and emotional characterization, a less mature and realistic tone and style, outdated sound effects, an overly iterated game engine, much less movement freedom and fluidity).
Those aspects were rightfully addressed by 343 with H4 Campaign and H5 Multiplayer.
The only thing 343i did wrong was too much mimic CoD MP formula hoping to cater a big chunk of the CoD fanbase to Halo, but this just resulted in loosing a lot of core Halo fan in the meantime...
Plus they really went too far hoping to smoothly pass the Master Chief main character torch to a new un-flashed guy like Locke and his uninteresting Co-Op friendz (except Buck).
Both things already addressed with Infinite :)
Now they really are on the right track for a truly next-gen Halo, especially considering the bold decision to step back to a more classic visual and audio design, while keeping most art style advances achieved with 4/5.
To make the Halo Combat...Evolved again, what it's missing and it would be amazing are exactly those most open area to explore and to fight in, more rich with life and details and beauty to just look at, alterned by a much bigger all-out war between different factions, and a much more big battlefield scope.