Most of this cost isn't the house, but the land. Lately I've been starting to think it would be a good thing to abolish private land ownership and replace it with a rent permit system as cities have increasingly become exclusive wealth zones.
What's progressive about paying 20-40% of your income in housing costs?
What's progressive about replacing private property with a system loaded with opportunities for graft and corruption? It's the poor who get the shaft when private property rights are not available as they can never be secure that what they do have will remain theirs.