There are ways to incentivize people to care for common resources. See the work of Eleanor Ostrom. Not to mention I've seen plenty of private property that is totally trashed.
Land ownership (or more accurately, expropriation of land by the wealthy) is one of the biggest roots of all other forms of oppression. Because you can't enslave people if they can just go opt out and live off the land. Many slaves historically did exactly that but the modern state makes this far more difficult today.