Premium clients can singlehandedly make a flight profitable (and in some cases, pay more for their last minute reservations than all of coach combined), so there's a damn good reason to wait for them.

As someone who has paid upwards of $8K for a last-minute first class ticket (6 hours booking to flight), I don't doubt this at all.

AFAIK whole airline routes are determined only by business class demand, not couch (except discount airlines).