If the price of uber remained low then it probably would have reduced car ownership. but the price has at least doubled making it unaffordable for regular use.
I'm not sure why anyone expected Uber to stay cheap. It's got the same costs as a traditional taxi, a car and a driver, so it's priced similarly to a traditional taxi.
Because in theory people could go out home without their car and don't create traffic while looking for a parking spot. What actually happened is that people who used to use transit, started using Uber instead, creating traffic where it wasn't before.