If you get rid of a lot of inefficiencies (unnecessary parking, land use segregation increase travel distances, and restrictions on multi family apartments), there will be so much more space available that it would lower housing prices by a lot for everyone. The tax revenues can also offset other taxes like income or sales taxes which also reduce inefficiency.

> it would lower housing prices

Moscow did just that in 90-s. They allowed densification without any regard for parking spaces.

Guess what happened? I give you three guesses.