The reason some locos depart at Dark O'clock is that allows a whole other rotatioin to be squeezed in during operating hours, if they don't do this, costs creep up and Joe Public realises this and trys a different loco making a false economy.
One reason Debonair went bust. Poor scheduling such as their daily LTN-BCN W pattern through LGW. Mid summer, leave LTN at 0800z when the others are on their way back or heading to the next destination !! Same with CIA, leave LTN 1015z. Madness.
Although this has changed to some extent. I remember when the German Locos set up shop at CGN a couple of years, the first departure wave was at 6 a.m. Even though public transport and road access to the airport is quite good so that passengers could make it easily to the airport at, say 4:30 or 5 a.m., departures were laterp pushed forward to approx. 7 am. Nowadays, there are hardly any departures before 6:45 a.m.