Because once self-driving cars are cheap enough -and they will be-, this model won't make sense. There would to many cars competing for the few clients that need rides at any given time. The money you'll make will probably amount to nothing and won't cover the hassle.
But I don't think this will be an option. I think we all know cars are extremely inefficient, but we fail to see the magnitude of that inefficiency. They are outrageously, extremely, mind-bogglingly inefficient. To the point that, once they start to become more efficient thanks to self-driving, owning your own car will be extremely rare.
The thing with self-driving cars is that it really alters the whole economic landscape of car transportation. You don't need two cars in your garage because the same car can take your kids to school and you and your spouse to work.
But keep that idea scaling. Your whole neighborhood could probably get around with less that one self driving car per house. So you'll start seeing neighborhood associations or apartment buildings pooling resources to buy 20 or 30 cars for the whole community to use.
Scale even further. The same could be said for a city. You could just have a fleet of 1000 cars, paid and maintained by the local government with taxes, that move people around with maximum efficiency.
It's not that Uber has a tough future ahead. All car companies that rely in selling cars in volume will also face pressure. There will be a lot of concentration, a lot of mergers and a lot of bankruptcies, because we are going to a market that will be 1/10th the size of what it is now.