Red-eyes from the west coast to the east coast work because of the timezones. Depart the west coast at 11:00 pm and arrive at the east coast at 7:00 am in time for a full day at the destination or a connection to the early morning departures. Westbound the timezones work against you. If you did it west bound you'd be departing at 11:00 pm and arriving 2:00 am; a schedule for which there is not a lot of demand.

The airplanes aren't underutilized overnight. That's when much of the maintenance is done. Scheduled service checks as well as fixing the problems that developed during the day and were deferred.

Of course, if airlines could make money by running significantly more red-eyes, don't you think they would already be doing it?