If this has a problem, it's the difficulty of application: 2nd homes, and only if you have X amount of money, instead of just a flat increase. Property taxes (or really, in NYC land taxes, as most of the property tax is really the value of the land) are just very efficient, and make much less of a difference on the price of rents than you'd think.

Unfortunately, doing that is very unpopular. Unpopular enough that we see states trying to get rid of property taxes, and those providing limits to increases, which basically guarantee misallocation and rising prices. But what is economically reasonable and what the voters like have very little to do with each other.