Maybe, but it might just push many would-be car owners to just use a service and forego buying a car altogether. What's the point of paying the capital expense, and a subscription expense for a car vs just calling up a Waymo. The traditional car makers should really be wary as they've historically been terrible at service offerings.
If you rarely drive using a service might be worth it. However if you drive more often it will be worth having your own car because it is ready when you want to go. I have a second car that I rarely use - but if I got rid of it a uber is 15 minutes away when I want to go, and the local rental car place is always sold out if I didn't reserve a week in advance.
Even if I'm using a service, someone needs to make the cars the service uses - the car manufactures are not going anywhere, they just get a different customer.
People said this about Uber 15 years ago, and well, that didn’t happen.
In the next step, somebody will notice that many people drive to the same destination (like a large shopping mall or an airport) and try to offer to take them in the same self-driving car for a discount. Over time those vehicles might grow to seat as may as 30-100 people and stop at multiple destinations