It can work out, it depends. How often do you need to use the taxi to not inconvenience your lifestyle? Are you the type that would have a new car or used car? more expensive. Would you do your own car maintenance? Do you life to vacation in remote places where you would have to rent a car? Do you have kids (no taxi has a car seat). How good is the local transit service? Is parking "free" with wherever you live and go (use it or not)? I'm sure there is more.
If I could rent a car and it arrived in front of my house, no need to own.
But if the nearest car sharing station is 15 minutes away, that just added 30 minutes to every car trip, on top of the friction that comes with such systems.
That's where self-driving cars may be able to make a huge difference.
Personally, I did use ride shares, but there was enough need for me that the math worked out for personal ownership.