I mean I paid for it like I would anything else I wanted. They charge a tax at checkout. So if I buy a house and pay the whole thing off, why do I still have to pay taxes on said house when I paid the whole agreed on price in full? It would be like me buying a six pack of beer I pay for it and tax at checkout. But then timely I have to keep paying taxes on the beer even though paid in full?
I’ll answer in a different way from others. Property taxes, in theory, ensure that the property within a jurisdiction is being used productively. Since you have to pay for the land no matter what, it’s a good idea for you to do something with it that’s productive. Even homes - it ensures that someone is loving theee and not just letting a house be empty.
In practice, that breaks down - speculation, tax writeoffs, taxes that haven’t been adjusted in decades all mean that people/corporations don’t give a shit and let property rot.