Building more houses increases property tax revenues, but it doesn't increase them per capita because now you have more people. The government's costs are per capita, so that doesn't help them.
By contrast, increasing property values generates more revenue per capita, so property tax gives the government a perverse incentive to increase housing costs.
Currently, people are already spending a really big part of their incomes on rent, and hence property. It is not possible that they'll spend any more.