Almost all cars right now are empty nearly all day every day. Vehicles that go around picking people up (cabs, buses, ubers, etc) are the ones that actually achieve utilisation of any significant amount. If more cars are shared, people per car goes down, not up.

Also, it's not as if those empty unused private cars disappear when not in use. They take up vast amounts of public and private space in urban and suburban areas.

Parking cars are not as big issues however as moving cars. Moving cars take more space, cause traffic, make noises.