The better change would be to change property tax law to only tax the value of the land, and not the improvements.
This conceivably could produce more housing: Same property tax payment, why build a three-bedroom house when you can bulid a six-bedroom house (or maybe 4 small apartments with 8 bedrooms.)
On the other hand, property taxes are necessarily the lifeblood of local governments: you can find and lien real property, it's there on the map that shows your city's boundaries. And property taxes are for police, teachers, firemen, etc. The more inhabitants, the more of these services are required. Who should pay that tax? Shouldn't the guy who's got 16 people in the apartment he built on his parcel pay more than the family of three on the same-sized parcel adjacent?