Cars in general are mainly used at both rush hours and are parked somewhere in between. Sharing cars won't magically change human behaviour.
Some googled "traffic by time of day" graphs: http://www.cs.utsa.edu/~cs1173/images/SATraffic3Intersection... and http://www.cmt4austin.org/Traffic_By_Time_of_Day.htm
The increase in ride-sharing has already greatly increased congestion: http://www.chicagobusiness.com/article/20180316/issue01/1803...
And out in the boonies, some people will keep their personal cars, as it will take longer to get a ride.
Also, the average car size will shrink. Not only will we lose the driver's seat, but peak demand as people go to work may be met with even smaller one-seat cars.
You won't need a car that can handle your worst-case scenario for most of the time. Bigger cars will still be available, of course, because people do like to travel with their friends and family whenever possible.
All in all, it's a lot more likely that that most seats will be filled.
taking labor out of the equation it will become cost effective to be empty an even larger fraction of the time (presumably humans stop driving when they're not getting enough fares to be worthwhile). It may also be economical for these vehicles to never park (not only because parking costs money or might be far away, but because it increases latency) for large fractions of the day.
