Depends on how you want to define land ownership, or how far back in time you want to go. But we don't have Homesteading any more. Squatters are legally evicted from vacant "unowned" land. The state lays claim on deeds when an owner can't be established. Then there's Eminent Domain.
Personally, I'd love it if property taxes were paid once at time of purchase. They already add on a deed transfer tax, a recording tax, a sales tax, and other fees for title search and stuff just to get a deed. Whether the state "owns" the land or not, they have legal authority to require all sorts of things to prove ownership, to require zoning, and to tax. They set the hoops and we have to jump through them.
Ditto for home ownership with a lien or mortgage---the bank owns it until we discharge the lien. We consider the house "ours" but it's really not.
You can buy land 5 miles from a mall and farm it (or start a junk yard, or host raves or whatever) but you've already agreed to follow the zoning laws when you signed the papers, and agreed to get a permit for certain stuff. (I have to pay for a permit to hold a yard sale, and can't have one every weekend. I can't have goats to eat my grass, or put a produce stand at the curb to sell vegetables, either. etc etc)