No, airlines do not arbitrarily cancel flights a few minutes before departure because of low loads, they are quite good at forecasting what the load and revenue will be well in advance and cancelling causes gross problems elsewhere, quite apart from bringing the CAA down on you and saying you don't have the resources to run your operation (cue dismissal of the Ops Director).
What does happen where there is a tech issue and you become an aircraft down is you make a judgement on how best to reorganise things to handle it. For example, assume there are two flights departing at 6pm one evening to separate destinations, one is the last flight of the day, the other has another flight at 8pm. Should either of the aircraft go tech or be grossly delayed inbound it is obviously better to scrub the one to the destination where pax can be served by the later flight, and put the remaining good aircraft on the destination where there is no alternative.
Likewise, say there are three simultaneous departures but you are suddenly one aircraft down. The loads on the three flights are 100%, 70%, and 30%. Which one do you cancel ? Can you see how the "because of low loads" story gets currency ?