The reality is, the implementation of policy such as this will definitely be advantageous to the society in different levels but it will be quite impossible to implement such policy in areas of the society without good public transportation because imagine large families with different destination for daily activities, they won't be able to make use of just one car for all, so they will need to depend on public transportation.
It might seem like a befitting policy with lot of goodies but it also restricts lot of advantageous privileges that comes with each individuals owning their own car.
Indeed... I even know some people that owns multiple car not to use them at the same time but because collecting car is part of their hobby and they will be the most affected if such law were to be implemented.