Yes, but historically capitalism has worked. That's the whole point here: things are changing. Not all of the lessons of history apply in a post-scarcity world.
"Those who do not learn from history are doomed to repeat it."
I'm not sure what you mean by "post-scarcity"? Things may be "available", but that doesn't mean people have access to them.
While it's nice to think of land as "unowned", in practice, someone controls it, and they almost never have the interests of the occupants in mind. Besides, I've found that people tend to treat property better when they consider it theirs and have space AWAY from people.
Going along with your point though, it might be best if everyone received some designed size plot of land (large enough to build a small family residence on at least). Yes, there would be competition, but in competitive areas, the land plots could be smaller. In "unwanted" areas (Kansas, Wyoming), plots could be large enough for profitable cattle and farming industry. The good thing would be that no one would be without land to built on; they would have their own space to "be them" and live as they wished without rubbing shoulders with their neighbors (which tends to make Americans rough around the edges, regardless of age/sex/political views). Currently, many people struggle just getting an apartment, let alone a house. Notably, the mechanics of a new system would need to be worked out, and would likely be abused, manipulated, and ruined because of selfish people, but it's a nice thought.
Yes, that's why I'm advocating leases. This allows you to separate short-term control from long-term control more easily. The interests of the occupants are best attended to via short-term control (the sink needs to be fixed now) but the interests of society are best attended to via long-term control (we need to tear down this single family house, which made sense 50 years ago, and replace it with a multi-family unit).
> it might be best if everyone received some designed size plot of land
That might work if there was a constant supply of new land to distribute, but there isn't.
Sounds nice, but good luck finding politicians and leaders who will exercise just (as in "justice") decisions in this manner.
More generally: The problem right now is a people problem, corruption. The system isn't the primary problem. If everyone were benevolent, sharing, kindhearted individuals, then we'd work together to see everyone had a home, regardless of whether the system was capitalistic, socialistic, or communistic. Instead, we live in a world of selfish people. sigh
It's nice to talk about theories though. :)
> That might work if there was a constant supply of new land to distribute, but there isn't.
True, but there is plenty of unused land. Just that people tend to crowd the coasts. EDIT: I didn't finish my thought. I meant to add that there's still enough earth for people to occupy for years... and we can build vertical realestate too.
It wouldn't work. Building codes and permits would make it too costly for the poor to ever do anything with it.