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?