OK, so you dont buy the plot and just build two houses on them. How does that change your logic.

How do you deal with a situation where some people don't have any land anymore to put their houses there?

They make something they can trade, or go somewhere where there is land.

How they can make something they can trade, if they have no land on which they can make it? Where can they go, if private property exists in most of the world?

You make things that don't need land, like 99% of humans on the planet. AKA get a job.

There's no free land, but there is cheap land, especially in deserts. Simply owning land might not be as nice as you imagine