Property tax is generally the purview of the states and/or municipalities, and is their primary source of income where it exists. Virtually all local jurisdictions in the United States have either a property tax, or a sales tax, or both. These are levied in conjunction with higher-level property taxes; here in Texas there's no income tax, but there is a rather hefty property tax; my bill on a $150k home in a not-bad neighborhood is $3,000, right at the low end of your bill for a half-million-dollar house. These taxes are the primary source of revenue for these smaller jurisdictions (and sometimes the entire State), and they pay for most or all of the following:
- Local road maintenance/signs/lights (the money from car registrations is State-administered and pays primarily for high-traffic state and federal road maintenance)
- Local first responders (police/fire/EMS; there's some federal money too, but it's spent where the Feds want it to be such as on counterterrorism and various modernization initiatives)
- Local government offices including courts (again, some federal money)
- Mass transit (obviously there's ridership fees, but your $3.50 for a day pass doesn't pay everything)
- Municipal facilities such as parks, pools, etc.
- Public schools (a pretty big line item, and the federal DoEd dollars don't pay half the cost of the average ISD)
There are federal dollars, other revenue sources (State lotteries often pay for schools), and "usage fees" at play as well, but basically property taxes are the primary way that cities and counties, and even a few States, provide you with the basic services that we generally agree government should provide.
The justification is eminent domain. It's very simple; when you buy land in the U.S. and a State thereof, you are still a citizen and/or resident of that State and the U.S., and subject to their laws. You're not creating your own country when you buy a house. As such, the government charges you for the facilities and services they provide in your area and your State, which are then your privilege to use. Obviously roads aren't free; a one-mile stretch behind my house is costing the county $15 million to expand it from 2-lane to 4-lane.
Here's the kicker; you've already been paying these taxes. You think your landlord's just going to take the taxes for the whole apartment complex on the chin? He's out to make money, and doing that requires charging a sufficient amount to cover costs, including taxes. You just never see "allocated property taxes" on your rent statement, just like you don't see "allocated landowner mortgage", "allocated facilities maintenance", "allocated gross margin" etc. You know you're getting shafted, paying someone else's financing with a little extra on the side to boot. That's why you want a house.
Unfortunately, not being able to pay these taxes is a grim reality for some people, old and young, and government generally doesn't go easy on delinquent homeowners. After medical bills and mortgage delinquency, property tax delinquency is the number three reason for bankruptcy, and only a mortgage or property tax delinquency can cause your home to be seized and sold. Well that and using it for criminal enterprise, but unless you're running a meth lab in your half-million-dollar home or financing it with coke money I wouldn't worry about that score. Retirement planners figure property taxes into cost of living, and they do often advise a downgrade from the 2-story house you raised your children in to something smaller (for many reasons, including lower taxes).
Play SimCity sometime. The taxes involved are basically property taxes. There simply is no way to create a completely "pay-as-you-go" city that has zero property taxes, and you wouldn't want to live in it if there were (imagine, for instance, every strip of asphalt from here to your work being a pay-per-mile toll road).