The biggest disadvantage to buying an empty leg flight is a lack of flexibility. Everything is predetermined, including the aircraft type, flight departure date, time, and destination.
Even when possible to make slight changes in the scheduled flight path, you’ll have to pay any extra airport landing/takeoff fees associated with the change. The flight dates and times, however, are generally quite rigid with little room for maneuvering.
Lastly, if you book your empty leg flight with only a few hours to spare, they may not be able to arrange your catering in time.