Many taxes have exemptions. You get a "personal exemption" on your income tax. You don't pay tax on 100% of social security income because of another exemption.
A "property tax" is a wealth tax that simply has exemptions for all of your wealth stored in stocks/bonds/anything-that-isn't-real-estate.
It's not though, it's levied on the assessed value of the house regardless of the stored value. A fully paid off house and a mortgage a month old at 90% LTV have the same property taxes if they are assessed at the same price. It would have been disingenuous to tell everyone who was underwater on their mortgages after the housing collapse in 2008 that they had so much wealth in the their houses based on the fact that they still had to pay property taxes.