I think it would be really, really cool if there was a better way to get rid of the HUD(as to have a more compelling atmosphere. Here's my basic idea:
Create a mode where you have a phone, one that can check the minimap, your health, the ammunition, the objectives, the dust you have. Pretty much every function of the HUD would be on the phone, but the game world is still active when you use it, and it would be on the scroll wheel(though wouldn't take up a weapon space).
I think this would push the game to the next level, like the hud-less mode in the metro games, but would also make playing hud free on expert difficulty an enjoyable experience.