Zoning issues are entirely local/state-controlled. Not sure what legal mechanisms the federal government could even arguably use to assert authority – keen to hear if anyone has ideas though.
https://www.businessinsider.com/treat-building-housing-like-...
Nobody at the federal level actually wants to fix this housing "problem" that's real issue.
Now that wouldn’t help you in a city like Boston or New York, but there are plenty of states where the federal government owns the majority of the land.
Whenever I pass reservations near major cities they are chalk full of stuff the city would never approve, that is actually affordable to build.
But give the historical relationship between the government and the Native American organizations, I can’t imagine most tribes would politically get behind using their limited reservation land to house people from outside the tribe.
Feds could ban or reform zoning just as they can ban me from growing and smoking a marijuana plant that never leaves my property nor enters commerce.
I'd prefer something that is somewhat less of a perversion of the Constitution, though. Find some other grounds on which zoning is unconstitutional. (The advantage of that is that governments aren't allowed to do what's unconstitutional, whether or not the federal government has the right to overrule local law.
Like, zoning might be considered a "taking". The government has taken from me the right to build a skyscraper on this piece of land, so they have to make "just compensation" - they have to pay me the difference between what the land is worth now and what it would have been worth if I could build the skyscraper on it. Making zoning that expensive could make it impossible for local governments to do it.