California

That will reduce prices by immediately keeping a lot of potential buyers out and by capping how much they can spend, but there will still be a bunch of places in the state where housing isn't being built because of height restrictions and similar. That's what the author is flagging as being the big issue, and I'd agree with him:

The first is these growth restrictions that first showed up in the 1970s and have gotten worse over time. I should note that some of these are finally being addressed in the California Legislature and in some cities.

Like, ordinarily, what happens if you don't have artificial restrictions on construction, if prices rise enough to the point that it's profitable to build housing, you get more housing.

What we've done is placed a lot of artificial restrictions preventing that construction from happening.

So when that happens, a housing shortage shows up. People bid for what limited supply there is. The poorest get priced out.

Larger loans let people spend more. So as long as there are some people who will take out ever more debt, larger loans will let prices rise even further.

We could block that, limit loans.

But that happens by excluding even more people from the market, just people who are a little richer than the poorer ones who were already being bid out. Like, if I cannot buy a house with cash, but can afford to do so with a ten-year mortgage, then I'm priced out under a "5-year max" proposal like the one you listed. That's not great, because it excludes a lot of people from being able to have housing when we could let them have housing.

It'd be preferable to build more and end the housing shortage. That'd let prices come down to a level that'd be more generally affordable---like, we'd prefer prices to be limited by supply always being able to catch up with demand, rather than by trying to artificially exclude people from being able to get housing.