Preferring cash payments and taxes already being good enough is not supply side. Once self-driving taxis are available, they won't be uber exclusive. More likely all taxis will become self driving. If uber wasn't in the market before, it won't become welcome just because.
In addition to that, part of taxis service is human powered. Like helping you get luggage in a trunk and providing local knowledge. A taxi driver in Japan once told me they make most by driving old people from grocery stores back home. Will self driving car have a robot helping them with the bags?
As a westerner with incredibly limited Japanese language skills, I've found the interactions with taxi drivers in Japan to be amazing. Showing an address or saying a name of a restaurant / landmark will get you taken directly there. Even sometimes when the taxi doesn't fit down the smaller lanes (in Kyoto) - the driver will get out and show you to the door of your destination.
In addition to that, part of taxis service is human powered. Like helping you get luggage in a trunk and providing local knowledge. A taxi driver in Japan once told me they make most by driving old people from grocery stores back home. Will self driving car have a robot helping them with the bags?