Probably nice for the US, but in much of the rest of the world, it is the price of land which dominate the price. Any system that aims to reduce house prices really need to deal with limited supply of land to build on.

Even on Iceland which has vast amounts of space and tiny population, house prices are high because the areas where people want to live is in high demand.

Now if you could just build your house at any arbitrary location on Iceland then that would not be a problem. But people needs schools for children, hospitals, jobs etc. That limits the options.

The US has fairly cheap land because it is flat, it is easy to build infrastructure and there are a lot of roads everywhere which you can connect to. The city planning also space out things a lot leaving a lot of land for building.