But let's ignore that fact, and instead look at a different definition of number of cars on the road: Instead of how many cars actually exist, count how many cars are on the road at any given time. It's not just that there might be more cars in the end, but even with fewer cars, each car will be doing more miles, because you don't need a driver. Children visiting each other while being less of a nuisance for parents mean more trips. Old people that are uncomfortable driving. People going further away in geneeral, because being driven would be less stressful when the technology is doing well. More visits to the bar, now that you don't have to call an uber, or risk a DUI on the way. And let's not forget letting the car go back home to park, instead of paying for expensive downtown parking: Same number of miles with a passenger, but bonus congestion for everyone else.
When driving is cheaper, the number of miles driven goes up, and therefore the number of cars that you actually find on the road goes up, even with fewer cars.
This could also play out totally opposite to that - think cheaper on demand rides, no need to park near your work if your car can just go do something else, etc. This might play out as actually less people owning a car, or families owning just one car instead of two, etc. I remember a prediction from a few years ago that it may reduce the number of cars by 80%, which I doubt, but I also don't think it will necessarily mean more people buying cars.