A property tax is not an income tax, it is a consumptions tax where the thing being consumed is the services provided to maintain the infrastructure for the homes (water, power, gas, roads, schools, etc). It is calculated via home values only because local governments have no access to anyone's income and cannot levy and income tax, so the price of the home serves as a clumsy and imperfect proxy for ones investment in the area and ability to pay.
If taxing unrealized gains is somehow “unfair” for billionaires holding stock, then why are middle class homeowners hit every year with rising property taxes based on the unrealized value of their home?
Most people haven’t sold their house. They haven’t “realized” anything. Yet the tax bill keeps going up anyway.