I think Snipers being a one shot to the body is fine, because generally most military sniper rifle rounds should kill with that, if im correct.
But the problem is the amount of versatility they have, if thats the right word. Being able to run and jump and be as effective and quick at close range, as a sub-machine gun wielding class, but having a one shot weapon is not right.
If your going to make your sniper rifles one shot to the body, make the player slower, and make scoping in times a bit longer too, the CS method of scope going from hip to eye, with perfect alignment every time in under a second isn't the right way to go about it in my opinion.
Im not army, I dont have a large experience in fire arms, but I know they are heavy! And getting the scope right takes a little bit of time. So to an experienced soldier it will be easier but still, not as easy as most FPS games make it, I mean firing a high powered sniper rifle just after running could break your shoulder!
TL;DR Make snipers less mobile and easy to use. Then yes!