There's no gap. The problem is that you're looking for a service that you don't want to pay for. Someone has to compensate the driver if he has to sit and wait for 20 minutes because it took longer than you expected to get curbside. There's also the practical issue of the Port Authority Police often not allowing limo drivers to wait curbside, and thus they are forced to circle or wait in the cell phone lot.

Don't get me wrong. I share your frustration. I often struggle with the question of whether to reserve a car or just catch a taxi. What sometimes happens is that I'll opt for a cab and get to the queue and find a very long line. I find that if I then call the car service (I use Elite), they're often able to get a car there very quickly (i.e., in about 10 minutes, but not in 30 seconds).

Elite used to (maybe they still do) have an arrangement with the US Shuttle that allowed Elite to line up cars outside US's shuttle terminal at LGA, so in most instances passengers could walk right off the plane and into a waiting car. (Passengers were not assigned a car number, as far as I know, but just got into the next car.) Perhaps a service like this could work at an affordable rate, but of course if it were to get popular it could just turn into another taxi line, where you couldn't predict if you'd get right into a car or would have to wait.