at the very least their drivers will still own cars.. if buying a car is all of a sudden not normal, then it would cost A LOT to become an Uber driver.
Car ownership is already not necessary. Both Uber and Lyft offer a car "rental" or leasing program where you will be given a car to use for the job for a fee which will be waived or reduced if you drive enough and do enough business with the car. They profit off of this or at least recoup money if you fail to hold up your end of the contract or in certain cases, you pay for the mileage you drive outside of work hours. This drastically reduces the capital necessary to start driving for these companies.
either way this drives up cost because it raises the amount a driver must make a month. obviously we dont have concrete numbers but if people are switching to uber only they probably would want to save a lot every month versus owning a car.