They do burden the airport to some degree though. The airport allows off-airport rental agencies to drive their giant billboard buses onto the premises, and also provides a curbside for them to load and unload passengers.
Clearly FlightCar doesn't burden an airport in the same way, however they do to some extent. Maybe if the airport worked with them and provided some portion of short term parking for their customers for a cut of the price it could be beneficial to both parties?