So instead of, say, having rush hour start at 4pm, with people leaving work, you have a new, free, bonus rush hour at 2, of empty cars driving near the places where they'll need to be picked up. Same thing near any other rush hour: Every added mile kills. It's not even just cars that have this problem: You'll find that in American cities with transit, which often are built with very few key destinations, there are large depots for trains downtown! Bart has no need to use most of their trains most of their day, so you'll find trains that just go downtown and stay there, parked.
What drives efficiency, always, is fewer miles traveled, and having the need for transport be as even as possible. Something like car-centric stadium is terrible: You need major infra to support a game, with many lanes, and many parking places, just to support game days. But then there might be as few as 10 game days a year, so all that extra infrastructure is wasted the other 355 days.
Self driving, rented cars probably make the first worse, and don't really make huge differences in the second. I think that they have advantages: fewer people dying from drunk driving, or someone doing 80mph in a city street running people over, like we had last week in St Louis. Younger people and older people retaining some independence in areas where now they are wholly dependent of others to go anywhere. But the efficiency gains story is a pipe dream. We will see more miles driven, and therefore more total congestion.
