They could just be Soldiers and give themselves ammo or get ammo from other Soldiers. You can also reload at Command Posts.
There are still ways to balance without totally nerfing it...
Grenade Launchers are heavy and slow but should still do a lot of damage. It should take an eternity to reload and only allow you to carry like 5 shells. Soldiers can only give themselves ammo so many times and if reload times are really slow it should help deter a person from going too crazy with it.