Consider a very simple city model which requires 10,000 cars to meet demand during rush hour (3 morning hours, 3 evening hours) and 4,000 cars to meet demand the rest of the time.

A self-driving model requires the up-front purchase of 10,000 cars, 6,000 of which sit idle 18 hours per day, earning nothing. Meanwhile Uber and Lyft have zero up-front costs, and only pay drivers when the company itself is earning revenue (and presumably, a marginal profit).

Who owns the AI-driven car? Who maintains it?

Either Uber is spending a shitload of money to build, maintain, and replace their own fleet or they‘ll be leasing cars from private car owners for about what they paid human drivers in the first place.