Most people have their property taxes escrowed with their mortgage payments. Taxes can easily account for 25% of one's monthly payments. As for rent, the property owners just pass the cost on to the tenants by increasing rent. So property taxes are related to rent and mortgage payments. Even if not included directly in the mortgage payment, it affects how much of a mortgage one can afford.
"It would be a massive disincentive to the wealthy, since they own the most property and are used to it being an asset not a liability."
I'm not sure about this. Just because they own more property doesn't mean they would be the most affected. The tax would likely be a larger percentage of a "normal" person's income for their own home and thus more impactful to them. Plus, if the wealthy are renting out the majority of the properties, then they can make up for tax increases by raising rents (because property tax increase priced more people out of homes (because the price drop was a drop in demand), increasing demand for rentals). I do agree that it should incentivize full utilization of rental properties. But I don't think there are enough vacant rentals to affect supply/pricing, but I don't have the numbers. I would think that most owners are already utilizing residential rentals pretty much at full capacity in the markets that are the tightest.