The best solution to this problem is taxing land value instead of taxing property. Land value taxes have a lot of advantages. They incentivize construction, disincentivize vacant lots, and they also remove the profit that can be earned by being an idle landlord, which is unearned income.
With property tax, improvements on your property are taxed. This makes construction less profitable / housing more expensive. With a land value tax, they aren't.
LVT also encourages nimbyism from people who don't want to move. If the value of their land goes up they have to pay more taxes, so they're incentivized to ban anything new from being built.
With property tax, improvements on your property are taxed. This makes construction less profitable / housing more expensive. With a land value tax, they aren't.