I think it's okay to complicate things, especially because for those that don't want to go deep it will always be "pick whatever weapon you have and shoot the enemy".
I mean, I finished the original trilogy without knowing about plasma pistols destroying shields/vehicles.
I think with the introduction of Equipements/more vehicles the damage type discussion becomes interesting to me. If we have like... 4 big ammo types that counter specific stuff (health, shields, vehicles, equipment, etc...) and then inside each damage type we have specific roles (up close, mid-range, long-range, power weapon, etc...) I can see it being VERY interesting. Remember that the Arena/Big Team Battle gap will widen with this game.
Also remember some of the most famous games in the world are complicated to a certain degree. Fortnite has quite some dept when it comes to their weapons/equipments, all MOBAS (DOTA2, LOL, etc...) are deep as crap, Apex Legends and Siege are complicated.... I think Halo will be fine.