The property taxes are small in relation to the value of the overall value of the property. Typically the increase in value outpaces the expense so the asset holder generally doesn't sell.

If you are saving to buy a house and renting you still have to pay the property tax but you don't have the asset. So increasing the taxes won't help the person saving but won't really affect the house owner unless they fall into the category of asset rich and cash poor which are usually just old retired people on a budget.

The only way you could tax people and have it work is via some tax multiplier for each property you own. However people would just spin up a company for each property to avoid the issue.

How do you ensure property is used effectively? In the U.K you used to be able to squat a residential house. If you didn't force entry and you kept it for 7 year or so without objection it was yours. It wasn't a perfect system in the modern age but atleast it was there until pig fiddling David Cameron who earnt more as a landlord than a Prime Minister decided to make it illegal.