Yes, it could work, if the town is flat, and you never need to go more than a few miles. Or if there’s a very good and fast bus network and you can carry bikes on the bus.

For example, somewhere i used to live, it had a free bus for the decrepit and old, that went around the whole town and passed every house. So if you wait long enough, the bus will take to your destination, door to door.

But even then, there will still be a few people who need their own cars.