You think taxi companies are paying for enough parking spaces to store most of their fleet at once? A lot of those cars are stored on the street in front of the house of the driver.

Also, the problem of storing something like 10k taxis pales in comparison to storing 100k+ cars. Some large cities have millions of cars. When was the last time you drove to a stadium concert or ball game? It takes hours to get something like 30k cars in and out of those parking lots when everyone is trying to use the same roads at the same time. It's absolute gridlock.

So to implement anything like what you're talking about you'd need a network of garages and lots in the periphery of a large city, and the road infrastructure that can handle 100k cars driving from outside the city to your home all in time to whisk you away on your morning commute.

For that kind of civic planning & engineering complexity you could just build public transportation based on trains, light rail and busses.