In the past BRS used to see a lot of Hercules aircraft from RAF Lyneham and Sea King helicopters from RNAS Yeovilton performing practice approaches. Lyneham is no longer an air base although Yeovilton still has some helicopters there.
About ten years ago when I had an airband radio I heard a 'discussion' between a Sea King pilot and local atc when the helicopter was sent away from the approach for a while because of a busy period for airlines. Something was said about commercial operations taking priority.
I suppose bmi regional don't want to take the risk of being sent away from the circuit for periods when the airport is at its busiest with incoming and outgoing commercial traffic. The quieter times, typically mid morning and mid afternoon, might not suit an airline that is already short on aircraft and crews.
That might also be the reason why in the past couple of years the Red Arrows no longer seem to use BRS for parking when displaying locally. They used to park up on the Southside apron along with bizjets etc.