I feel like there is a solution that everyone would be happy with. It is to allow many new homes to be built, but to compensate existing homeowners for the fact their property will go down in value due to the influx of new homes.

For example, the law could say "Property taxes on all properties built before 2021 will be reduced to zero, while all properties built after 2021 will have to pay property tax at 5% of the property value for 30 years, before dropping for to 0%".