The local airport has similar issues with Lyft or Uber, which are in a separate zone from the taxis, so if it were possible to optimize better they probably would've tried already.
Autonomous vehicle “drivers” don’t need to shower, use the bathroom, eat or sleep, so instead they can be constantly moving rather than camping at airports. A car in motion is generating revenue, so I think autonomous taxis would be fewer in number than human taxis as well as behaving in revenue-optimizing ways (i.e. not camping at the airport.) Theoretically, those airport taxi villages would likely turn into charging stations with a few employees to provide necessary services.
Not necessarily. A lot of the self-driving taxi utopia is based on the idea that self-driving taxis will serve commuter traffic. And the major facet of commuter traffic is that you're going to have a high-volume, unidirectional traffic flow--once that car drops off its worker, there is no demand for it make any trips nearby. So if that car is in motion, it's still not carrying anybody, so it's not generating revenue.
It's sort of like congestion pricing.
Uber has done some of this already.
I suspect these are more easily solvable since there is more flexibility about parking spots (the cars don't need to be within walking distance and only a few need to be close by). But there will still be idle cars that need to be put somewhere during off-peak times.