Couldn't the parking be organized by just putting roboticized "air garages" to the top of sky scrapers? Carriers operate a fleet of aircraft in a very constrained space. With purely VTOL craft there is no need for that to be horizontal, it all could be put to vertical.

So you would have

1. Landing bay (helicopter pad or an enclosed bay).For enclosed bays those could be stacked on top of one another.

2. Robotic parking

3. Air control system to facilitate traffic and parking.

I'm not saying this is a necessarily a good idea. But I would love to know why it would not work.