It's usually factored in to your rent, so technically you do pay those taxes even if you're only renting.
Your house (usually) exists in a community where you have to use the roads, traffic lights, street lights, schools, municipal services, etc. etc. etc. That costs money.
Those costs are separate from your mortgage/homeowner's insurance. You may have a contract where your property taxes are factored into your mortgage payment (like mine), so it's not like you start paying property taxes only when your house is paid off. You pay it the entire time.
First world countries also do charge property taxes (several do so at much higher rates.) There are definitely countries that don't charge property taxes, but is the standard of living the same?
What else are you willing to give up in order to not pay one specific tax?