You pay taxes on the assessed value of your house. It doesn't matter what you paid for it, or how much equity you have in it. It's more of a use tax than a capital gains or wealth tax.
Also, just to add to the above discussion, it's even worse in practice than a tax on unrealized gains because I'll have to pay the same amount of tax every year if my house stays the same value. If it were a tax on the unrealized "gains" of my house, I'd pay $0 if it stayed the same value. And if the value of my house decreases, I'll still have to pay more than $0 in property tax, whereas a capital loss would mean I would pay at most $0.
So, I think I still stand by my sentiment that property taxes are more burdensome than a tax on unrealized capital gains.