I don't really see how it's possible since the plane probably has a lavatory for the pilots.

Maybe those were taken out so that the plane was capable of carrying more packages.

It costs money to have a contractor service the lavatory waste tank after every flight.

Since the lavatory is not on the Minimum Equipment List, it would cost 30 minutes of paperwork to update the maintenance log and declare it inoperative.

Depends on how much of a psychopath the person doing the cost-benefit analysis is I suppose.

Cargo airplanes typically don't.