>Property taxes would be levied on the owner, and be directly tied to house value.
That is awful, why would you ever want to introduce such a regressive policy? Higher density construction generally costs more than low density construction. Each floor adds more cost because you need proper ventilation, elevators, stairs, etc. Therefore an apartment will be taxed more despite having the same number of square feet/meter. Despite this, apartments still make sense economically if the land value is high but if you're burdening them with yet another heavy tax then people will shift to single family homes instead.
Then there is the fact that you should never tax someone for improving their house. Oh you installed solar panels on the roof for $30,000? Lets tax that! The solar panels are no longer a net gain. Homeowners no longer have a reason to improve their homes. Imagine someone working on his house in his free time. At that point you're taxing someone's free time. How backwards is that?
Stop taxing property value. It's regressive. It's a moral hazard. It doesn't work.
If you want to tax something, then tax the land those buildings are sitting on.
Bonus content:
And since for some reason grandmas are the most important members of a gentrifying city we can even take a look at what happens when they get priced out from a property tax vs a land tax.
Grandma sells her overpriced home because she can't afford the property tax: She can't move into an apartment because the apartment is taxed even more than the home she left.
Grandma sells her overpriced home because she can't afford the land tax: She can move into an apartment because the apartment is taxed less than the home she left.