Cars are high fixed cost capital goods. A taxi will be driven far more over the course of its lifetime than a personal car, so the fixed cost per mile is much lower.
Also, economies of scale make purchases and maintenance and repair cheaper.
These are two reasons to believe taxis should be cheaper than personal ownership.
Finally, let me point to airplanes. It makes far more sense to rent an airplane than buy one because almost no one travels enough to justify the purchase. Cars are analogous.
Edit: When I say cars are analogous, I mean that there are analogues between the situations. Both are vehicles with high fixed cost that can be either bought or rented. The situation is comparable, though obviously not the same. All I'm saying is that it's conceivable that someday the conditions could change so that it's more sensible to rent than buy.