There are two related issues: drag, which would slow down an aircraft and increase fuel needed for a mission and weight.
Looking at the second: say bomber X could carry 3,000 lb bombload to Berlin from bases in the UK. To get the required damage to the target, 150,000 lb of bombs are needed. This is 50 aircraft each with ten crew members. Get rid of the waist guns, saving their gunners (400 lb), guns, mounts, and sights (400 lb), and ammunition (200 lb), each aircraft can now carry 4,000 lb to Berlin. Now, there's only 38 aircraft required to perform the same mission.
Of course, now 1,000 lb more fuel can be carried in lieu of the bombs, which would permit more flexible routing or missions to more distant targets.