So if they invent the first reasonable self-driving car, they can sell those and provide service for them. Ideally TCO would be lower than a human driven car so basically a third party could buy and manage the fleet for Uber and Lyft. Neither company would need to own the cars to reap the benefits of making them.
They could, but that’s a completely different business to building middleware to facilitate unlicensed taxis. It’s like saying “AirB&B will help people rent their spare rooms out until they launch their own hotel chain.”