You'd still have campers. The only thing that would happen is that those (crouched) snipers far-far away would be collecting headshots left and right if the attacking team couldn't go prone.
If I get to the obj and die because there's a semi-hidden camper (prone or not) right next to the obj just inform your squad/team then flush with grenades, etc.
Oh, can't wait to test caspian border, even last night I was watching some youtube videos of it. Platoon! Form up and join the fray!
On the prone camping front i am with homerdog. The problem is people are always sensitive about their stats in game. Being able to prone camp introduces additional risk for advancing players (its always harder to kill someone in prone position than crouching) and also encourages players to gather kills rather than objective points (because you are harder to kill and have better accuracy laying down on the floor). If you combine this with indestructible bushes (see the deadliest bush vid) and higher bullet damage, sooner or later you will get WW I style trench warfare.
Dont get me wrong, i like the game very much (i even preordered it after few hours of beta play - my first preorder ever!). Its just i think that it would be better w/o prone camping.