Also, it should be noted that most airline hubs in Europe such as Heathrow, Paris CDG, Amsterdam, Frankfurt, Munich, etc... have overnight flight restrictions.
If there weren't such restrictions we might have seen 01:30 CET departures from Europe to New York and arrivals around 05:00 EST which could have a demand since US airports usually don't have overnight restrictions. Same thing would apply for flights to/from the West Coast. A 01:30 CET departure from Europe and an arrival at 05:00 PST could also make business. Not related to this subject but if Norse Atlantic or a similar airline trials this from Gatwick ( which is open 24/7 ) they would see the demand.