However many of the ad hoc freighters which make up the majority of BHX pure freight flights arrived before 11pm so not as much night disruption as you might think.
Not being funny here, but with the airport being closed at 2300, do you think that may explain why most freighters were in before 2300?
Of course only the few that could get in before then of course, most operated to EMA,SEN,CVT,DSA and LPL, all flights that previously would have operated through BHX.
Many flights operated to those airports even during the times that BHX was open, because the nature of ad-hoc work meant that they could never be guaranteed to arrive before closure, and arrangements for handling/trucking/customs/screening(for outbounds), etc would have to be made beforehand, not at 2305 when the aircraft is turned away from BHX.