Even with the APU running, it may be hard pushed to adequetly cool a full aircraft (I guess that Nice in June is warm!). With doors closed and no APU, the temperature will soon rise to unacceptable levels. (At least on the 737 classic).
Assuming there was a slot delay, the crew can ask ATC to put in a 'ready message', meaning that they are ready to go. In that case the slot could be cancelled if the flow controllers see that letting the aircraft depart now will not cause congestion downroute. Accordingly, doors have to be closed and steps removed to allow for an immediate pushback and start.
This is often the same reason we see passengers on 'Airline' and similar TV shows, having missed the checkin complaining, saying 'I can see the aircraft on the ground and it hasn't left yet, so let me on.' It is probably ready, waiting for a slot improvement, and won't risk losing that to allow late pax on board!