The problem is not competition from traditional taxi companies (they do indeed replace taxi companies' management structure) but other ride sharing companies, ie Lyft. Uber has only managed to stay ahead of Lyft by undercutting Lyft's prices, incurring severe losses in the hope that as soon as they have self-driving cars they will be able to become profitable by eliminating one of their main expenses, the drivers themselves, while maintaining lower prices than Lyft.
Without self-driving cars, that strategy isn't sustainable, and so eventually Uber will find itself unable to maintain its advantage over Lyft.
Without self-driving cars, that strategy isn't sustainable, and so eventually Uber will find itself unable to maintain its advantage over Lyft.