The way I see it, this is basically a squad dropping their Vet, and having another squad pick it up and instantly become elite troops. The MG 34 DPS is supposed to represent their skill, having it capturable defeats that purpose and the squad DPS is lower than LMG Grenadiers without it. If they lose their LMG, they become near useless as they can't even take on BAR Rifles confidently. If it's going to be droppable, then it needs to be nerfed heavily and that damage output 'transferred' to their Kar 98's to make up the difference.
Hardly. They still have armour, a received accuracy modifier, great vet bonuses, grenades, booby traps and the like.
Obers remain a versatile if not very impressive raw damage squad without the MG34.
The important thing is to be bloody careful with them. If you lose enough men to drop your MG, don't pick it up and then retreat, consider the massive bonus your opponent can get payment for how massively powerful Obers are.
Allowing them to drop such an important item is your own fault. OKW are supposed to be all high risk/reward, after all. Sturmtigers n'all that.