I think San Francisco is still bitter at Uber and Lyft for succeeding without permission, and has given their competitors a random handout as a poke in the eye. That’s the only way this “no cars on Market except taxis” rule makes any sense.
Other taxis operate on a government license, so this isn't really bitterness.
In Utrecht, Netherlands only busses and taxis are allowed in some parts of the city center, and this predates Uber/Lyft existing (let alone expanding to the Netherlands). It's pretty standard municipal policy.
> I think San Francisco is still bitter at Uber and Lyft for succeeding without permission
Have they succeed though? Last I saw, neither was profitable, and both were hemorrhaging hundreds of millions (and in Uber's case, billions) of dollars every quarter.