Why not wait in EDI? The answer is likely - schedule integrity. It is a low cost carrier which means they don't have spare aircraft lying around so an aircraft can sit around and wait. The airline would not allocate any extra time in the day schedule for delays, the aircraft has to operate other routes and flights, not just your grandsons. If there is a chance they can get in, the chances are they will depart (if they can do so legally).
Why not leave passengers on in BHX? Again schedule integrity. The chances are operations will plan for the plane to leave BHX > BRS, and if they can't get in go onto the next scheduled destination of that aircraft (BFS?) therefore having some small attempt of annoying less passengers. If you still have passengers on board then what do you do if you can't get in the next time round?