Thanks for the comment, Avraam. I wish your solution would work, but I can't see how it would since most human are status-seeking. There are plenty of homes. I've written about this in other pieces. And you can watch many YouTubers drive by empty neighborhoods of perfectly livable houses (with a touch of TLC).
When people say "Housing Shortage" they mean other things, like "why do you get to buy a home and I can't?", "why can't I live where you live", "why can't I build a home at the edge of your really nice neighborhood.", etc.
The Fed's primary role, since it's founding, is protect the banking system; that is, protect the assets of the wealthy. Everything else is just nice to have ;)