I thought that at many airports the longstay parking was provided by independent operators who provide shuttle services to and from the airport, and so provides little income for the airport.
At Luton the car parks are owned by the airport but the staff and coaches are provided by a third party.
Regarding the comment that the airport prefers people to park their cars rather than use public transport that would be true if Luton had the car parks but it doesn't. Also there is the issue of too many cars arriving at the airport at peak times which is probably the main reason for the council spending £200 million on a rail link to the station.