Are Uber Elevate and other air taxis subject to domestic ownership and control rules?
The most important thing to remember is that currently there is only one FAA regulation about person-carrying autonomous drones: it is simply not permitted.

Both 14CFR Part 121 (airlines) and Part 135 (charter/air-taxi) have ownership and citizenship requirements. (It is of course not known what Part person-carrying drones would be under, but we can assume similar requirements.)

However why should this affect Uber? They do not own the cars that are currently in the fleet; in exactly the same way they could have the aircraft be owned not by Uber, but by some sub-contractor.