It was Freeman Dyson who suggested that turrets be removed. ( I have quoted him several times on here re that subject in the recent past).
As Wensleydale has said no doubt the bombers would have been made to carry more tonnage to the enemy, thus cancelling the advantage that the weight/aerodynamic savings made. Some Bombers were stripped of all their armour plate to carry more tonnage, despite the pleas of the crews. It must be remembered that 'Tonnage ladders' were published and it was a competition between Squadrons/Groups to see who could deliver the most. I daresay many a senior promotion was won on that data and one wonders at what cost to aircrew lives?
Bomber doctrine ment that gunners and turrets would not be removed, as it was of great psychological value. Later in the war Dysons team interviewed evaders to get an idea of how they were shot down. The information they got was of limited value, they never saw a fighter, just a burst of cannon fire, then the bomber on fire around them. They had not realised that the bomber was a victim of Schrage Musik.