Property tax is a tax on specific property (usually we are talking about real property, but I've paid e.g. property tax on a car). It is usually irrespective of wealth.

Someone who buys a house with cash and their neighbor who is underwater on their mortgage and at risk of insolvency will pay the same tax.

Note also that you rarely see property taxes on e.g. valuable jewelry because unlike real property and cars, both of which have ownership centrally registered, jewelry is not centrally registered.