Considering the fact that HCEA is made using the engine from Halo Custom Edition, they could do all sorts of things when remastering it. I would love to see what you're suggesting, but with some added extras, like maybe more accuracy for the Assault Rifle, a slightly powered-down Pistol, and the addition of maybe... I dunno, the DMR or the Battle Rifle and the SMG to balance it out, along with the Covenant Carbine or the Needle Rifle and maybe the Focus Rifle or Beam rifle to help keep things interesting on the enemy side as well, along with maybe some new enemies like Brutes and Skirmishers, and Jackal snipers (Reach or H3 era type, of course) and Engineers (which were planned for Combat Evolved anyway but ended up being cut), as well as new vehicles like the Mongoose and the Gauss Warthog and even the Falcon, all of which were featured on the colony of Reach when it was attacked and thus should have been stored inside the Pillar of Autumn since it was docked there. But most importantly, I would love to see them adding the ability to swap weapons with Marines, hijack vehicles, and even use that visor zoom that was introduced in Halo 2.
Of course, it's highly unlikely that this will ever happen, so... I'll just have to play SPV3 for that feeling instead, even though it lacks the visor zoom and weapon swapping mechanics that made me forgive Halo 2 and fall in love with Halo 3.
Oh yeah, a remastered Halo 3 would be nice as well, I guess. I actually think it still looks pretty nice for its age, all things considered.
But yeah... it's unlikely any of the stuff I just mentioned will ever happen, but a fan can dream. A fan can dream.