It isn’t just rent seeking, it is regulation to try to compensate for the negative externalities of a private ride hail system (ie. Induced traffic).

Part of the origin story of taxi regulation is the fact that in the early 20th century unregulated cabs caused an explosion in traffic congestion. People complained and so the amount of cabs was limited. An example of the tragedy of the commons.

I expect that eventually we will see the same thing with Waymo etc but we’ll see.