Abolishing private property, in practice, generally creates more problems than it solves. How do rights and duties get negotiated? How does waste and disuse get managed? The backstop of land ownership historically, is who can violently eject others from their bit of land, or failing that murder them. Much of civilisation has accrued to avoid that, though it still the final degree of disputes.
Graeber's Debt: The First 5000 Years goes into the anthropological record on money, finding it emerged as debt not barter. Networks of reciprocal social obligations, underpin systems in which currency and ownership occur.
Graeber gave a talk Imagining Alternatives: Indigenous Societies' Perspectives On The Modern State, talking about his doctoral research on the human arrival to Madagascar and the culture there, and various Native American cultures, with interesting things to say about different models of ownership (eg 'Indian giving'), and the cultural reaction to enslavement in a world with large amounts of land with no humans on.
I'd say it's misguided to think of land ownership as one thing, or kind of thing. Many different types of agreement have been made, many different enforcement mechanisms involved with them. I would look at these as sets of answers to problems that typically occur in communities over land use, rather than as a single practice or concept.
An idea I have heard in the context of people suddenly needing to grow a lot more food locally when global supply chains break down, is to recover the Roman concept of being able to hace 'usufruct', or 'use of the fruit'. A bit like a food-growing leashold, that doesn't give rights to do other things with the land. That would address anxieties people may have preventing fallow or disused land from being used to grow.
Another case is the absorption in the UK of much of the ancient commoning system into the National Trust. This was largely about conserving wild places & traditional land use, rather than being ideological.
