There's a lot of truth in that, but it's also an oversimplification.
There is plenty of cheap land in California, here, have a quarter acre lot for $15K:
https://www.redfin.com/CA/California-City/Princeton-Ave-9350...
Of course it's cheap since nobody wants to live there. If everyone wants to live in San Francisco, it's going to be much more expensive. Building more helps but in the end there's only so much that can realistically be built in 50 square miles. Some people will always be left out so there will always be some unmet demand, so it'll never be dirt-cheap.
So yes policy obstruction is a thing, but there are also inherent reasons why popular places will never be cheap.
I guarantee you're not talking about homeless people here, but people who live in a home that they are renting, reasonably near the place they work.
edit: also, somehow these so-called poors are always wealthy programmers trying to buy million-dollar houses.
Housing is only "scarce" in desirable places, and that's simply tautological. The sum of unfulfilled desires is the contrapositive of scarcity.
Housing is a market in which a very tiny percentage of goods are up for sale at any particular time, and the projected prices of those goods are heavily shared among a huge network of people who profit when the prices are high. The owners of those goods are often heavily leveraged, and can't afford to lower the price significantly, and the transaction and mortgage costs push them to raise the price to cover those costs at the next place they buy.
> They can only extract so much wealth from housing before people move for alternatives.
No such alternative, which is why the market is as lucrative to exploit as health care. Finding an "alternative" to health care is just to find another type of health care, and if you find an alternative to being housed, you've just found a new kind of house.