Operations researchers found that heavy defensive armament on bombers increased casualties in a heavily defended operated: the increase in weight and drag slowed bombers, so more were needed, and the large crews meant that the number of casualties with each aircraft lost increased.
While this was, no doubt true, I think it overlooks a different problem: before smart weapons, massed bomber raids were necessary for the sort of suppression a couple of aircraft with smart bombs could do today: even if, as I've seen written, a Mosquito could deliver the same mass of bombs on Berlin as could a B-17, a 500-Mosquito formation would not be able to use the Mossie's superior speed or maneuverability to escape. The USAAF also found, quite the hard way, that bomber defensive armament, no matter how massive, could not reduce aircraft losses to a sustainable level. I have no real way of reliably analyzing the data, but I suspect that, had the USAAF removed the waist gunners and their associated weapons and ammunition, the numbers of bombers lost would not have changed, as each bomber could have carried 500 lb or so more bombs and, with the big holes that waist gunners shot through closed up, been slightly faster.