Not so fast. This may seem like a good idea at level 1 - the basic level.
Here are the issues:
The type of insurance you will need to buy to protect your vehicle, the occupants and the public. Not many plans will support an unlimited list of 'nameless' drivers.
Usage of the car - you will have no clue how the car will be used. For delivering banned substances, as a getaway car from a bank heist (Baby Driver!) and for any form of criminal activity. Perhaps even for a romantic car romp (eew!).
Care for the car. You seriously expect a stranger to take care of the car as you would? Not drive at high speed over road humps? Drive with the accelerator floored? Rapid start and stops wearing out the brake pads?
Cleanliness. What's to stop the users of the car from consuming food & drinks? Spillage of fluids. Infestation by vermin - cockroaches.
Availability. Will the car be availble when you need it? Or will you be stuck with premium pricing during peak usage hours?
As a public facility, this may not work very well.
It may work on a federated/consortium blockchain where the users are registered & known to the owner. The owner may need to install in-car & dashboard cams and the renters need to agree to the loss of privacy.
I don't know. Perhaps not the best use case?