The Power of Pricing is a thing that exists whether you want it to or not. Smart policy uses it to great advantage. Dumb policy redirects this to hurt those it intends to help. Rent control, restrictions on production, byzantine zoning and construction rules... all contribute to distorting the market in ways that push back on the original (or at least, stated) intentions.
You want housing to be cheaper? Increase supply. That's it. You don't want foreign investment in your properties? Don't make them so damn attractive as pure investment vehicles. How? Increase supply.
There's always a boogeyman to be blamed when markets are so broken like this.
Drastic? Well, then: kill NIMBYism. Just off with its head. We know the 18th century in England as the "Gin Craze", future generations will look at our period as the "NIMBY Craze".
Large-scale construction is absolutely possible. There were periods of massive construction booms all around the globe, especially after wars (when a lot of housing had to be rebuilt immediately). You can absolutely build a lot of comfortable middle-class housing in a fairly short time. Most German cities were rubble in 1945 and fine again in 1960.
But you need density and straightforward approval processes. No artificial scarcity caused by one-family home zoning and endless environmental reviews that are abused to stall developments for decades.
The USA (and maybe Canada) has large stocks of government land. In my country, most land is privately-owned; interfering with landowners' property rights is seriously destabilising. Property law is the basis of most law.
There are loads of cheap houses in the USA. They're just in places where most people don't want to live.
Here's a cheap house:
https://www.zillow.com/homedetails/420-Tyler-St-Gary-IN-4640...
The commute to Southern California is pretty killer though.
Maybe the USA and Canada could do something similar? I find it ironic that it’s primarily Chinese investors who want us to keep our property markets open.