The thing is there is no reason that companies could not be, at least theoretically, profitable charging rates that are actually less than it would cost for an individual to own a car. Without a driver their only overhead is the maintenance/insurance on the car itself. And that's something owners have to pay as well -- with the major difference that thanks to economies of scale the taxi monopoly could pay substantially less for. The company that has the most cars will be able to offer faster rides and offer them cheaper.
The potential profit here is really quite incredible. Last year there were 3.2 trillion miles driven in the US alone. Imagine a taxi company is able to snag about 1/3rd of those or about 1 trillion miles. Their profit margin translates to $10 billion net per penny/mile of profit.
So if they can, through economy of scale, operate their vehicles at $0.05/mile less than an individual owner could. And they then sell their service at a $0.01/mile less than what it would cost if you owned the car, then they're turning $40billion/year net. And that's again with 1/3rd the driving market. When you can offer taxis at below ownership prices, who would still own a car?
Tesla seems to be flirting with the possibility of taking this one step further will full vertical integration of production itself. It's already in their license that you're not allowed to use their vehicles (in what will be full autonomous mode) for any ride sharing service except for their yet-to-be-launched one. Interesting future coming up fast!