They could do it through community land trusts, which is basically where a nonprofit owns the land but leases it to the tenants at very low rates with the purpose of keeping housing affordable in perpetuity. One of the ways community land trusts get land is by having rich people donate it to them and then deduct the value of the land from their taxes. One reason coop housing doesn't get built as much (in the US at least) seems to be that coop housing used to get more funding from local governments, but local governments have favored low income rental housing construction for several decades, because of these getting tax credits that housing cooperatives don't.
Limited Equity Housing Cooperatives
Tax Credit

There's plenty of land, maybe just not where people want to live...

> There isn't enough supply of land

I live on the outskirts of the Atlanta metro area. Beyond where I live, there nothing but undeveloped forest. Developers have been gradually buying up and building, which is how Atlanta has grown. My little town has a "seed and feed" store and a Tractor Supply store. Both of those cater to farmers and large land lots, not 1/4 acre suburban. They would not be here if there weren't the kind of owners they cater to.

> Your plan only works if the person has enough capital

I'm an engineer, so I had enough income to do it. But not everyone does, which is why I mentioned a cooperative approach. People pitch in a little bit each, plus their labor, and fix up or build one house at a time to start with. One of them takes out their share and buys it conventionally. The loan proceeds then return the capital to the group so they can work on the next.

If you get one member like myself who has the spare capital, the other members don't have to contribute anything but labor.