The cheapest housing costs are found in rural and exurban areas. These jurisdictions tend to be overwhelmingly Republican. Now, does that mean that Republicans are more enlightened when it comes to affordable housing? No, it simply means that land is cheap as hell and nobody wants to live there. But is it affordable housing? Yes, yes it is.
Now, if you define “affordable housing” to be “public policy designed to accommodate lower income workers’ housing costs in expensive major cities”, then yeah, Republicans are awful at this. But it’s not like anybody is actually good at it.
Nevertheless, the law of supply and demand hasn’t gone away. If you keep building more supply, to the point where it saturates demand and then some, then yes, you’ll see housing prices go down. It’s pretty cheap to live in Dhaka, but you’d be living in one of the densest cities in the world.
In public policy, there are two ways you can make it cheaper for people to live in a certain area. You can either build as much as you can to keep up with demand, or you can allow the place to become so awful that nobody wants to live there (Detroit, New York in the ‘70s).