Many USA airports have an exclusive deal with a single "Airport Taxi" company ... anybody (even other taxicab companies) can drop off passengers but ONLY the approved Airport Taxi company can pick them up.
The way it works in the New York Metro airports is that all taxis must go to the taxi stand to pick up the next available fare. However, the traveler can arrange with a car service to pick them up at the passenger pick-up area by calling and requesting a car at a specific time. However, the car service cars are not allowed to pick up passengers for which they do not have an arrangement.
There are hundreds of car service outfits in New York who do a nice business doing just that.