Why is that? Taxis have always existed, and rationally are cheaper than owning a car for some. Yet most people own private cars, and when yours in the future comes with a free private driver, the possibilities for having a decent office or entertainment center in there when freed from the driving task will only make them more attractive to own.
Taxis mostly seem to displace other forms of public transport.
https://www.citylab.com/transportation/2019/01/uber-lyft-rid...