What would be so hard about allowing a new Uber/Lyft in for each leaving one, physically or logically?

Uber/Lyft could allocate the "new car in" slots using whatever mechanism they currently use to match riders to drivers.

Having to find "my" car is just completely backwards in the airport scenario, at least at times of high usage.

Because cars aren't allowed to idle at the terminal. They wait in a queue in the parking lot until they are matched, and then come pick you up. Yes this means you have to wait a couple minutes extra, but airports enforce this rule for a reason.

> airports enforce this rule for a reason.

What is that reason, and why are things handled so differently for taxis?

Have you tried writing to your local airport authority and asking them the reason? Or are you automatically assuming that there's a grand conspiracy at play against you?

In most cases it's a simple capacity problem. Taxis have to be hailed physically, and there are already reserved taxi stands at every airport. There's no reason for that to change.

I don't think this is a conspiracy at all, just a pretty standard case of an incumbent getting preferential treatment (why else do taxis get a reserved taxi stand, but Uber/Lyft don't?) and an "innovator" disrupting at any cost and externalizing the consequences (in this case congestion throughout the terminal and surrounding streets).

A more efficient stable state is clearly not being reached through market forces, but since there will never be agreement on whether that's due to too little (get rid of the medallions!) or too much market liberalization (ban the rideshares!!), and the only thing everybody can agree on is that a public transit solution is impossible, I don't see any way out.