LOL, that didn't even enter my mind. What I was thinking of was a smaller turret as the quad .50 turret caused aerodynamic problems.
Why bother? The tactical environment was completely different.
The Germans needed Schräge Musik, because it was taking down large night bombers. It made it safer for the nightfighter, letting them creep up into an attacking position without risk form the rear turret.
And it meant they could carefully hit one of the most vulnerable parts of the aircraft, without hitting the bomb bays, which was much more dangerous.
Naturally it was useless in daylight.
Now by mid 43 onwards the tactical requirement was for an allied nightfighter that could takeout Luftwaffe one, plus hitting the small numbers of twin engined night tactical bombers that might be encountered after the invasion. There were no hoards of German night bombers, or day bombers to fight. Plus the British had more than enough for their defence.
And that last point is a key one. By the end of 41 it was clear the majority of the German bombers were tied up in the Eastern Front and that the British were rapidly building up their night defences to a point where any further Luftwaffe night bombing attempts would suffer tremendous losses (as did happen). Plus they had good operational feedback from the success of the Beaufighter.
So what was needed? From the British experience with night fighting (and their own experience later) that was a better Beaufighter, something fast, with good forward guns, good range, good radar, good speed and agility.
A turret? Just weight and drag to slow it down, reduced its range and completely useless for any conceivable tactical environment they might face.
Now if by the end of '41 they had looked at that actual operational information and changed the design (which was incomplete at that time), stripped it down to 2 people only, got rid of the turret, did a radical weigh reduction program, improved pilot and radar operator visibility... they they could have had something pretty good and a lot faster than they did (basically a Tigercat like plane a couple of years before the 'real' one arrived).
But they soldiered on with an obsolete operational requirement, the rest as they say, is history.