Housing is treated as an investment these days, instead of as housing. That's the fundamental cause of unaffordability, and it exacerbates the problem. It's easily fixed with the right policies, but at this point it can never be fixed (with a huge political left turn, maybe).
Making it easier to obtain leverage doesn't make housing cheaper, it just makes the prices go even higher faster.
It's the same with money, when money deflates it's treated as an investment too, not a medium of exchange.
Just like housing being too expensive ruins it's ability to provide housing for everyone, money being too expensive causes a recession and unemployment.
The difference however is that money can be created through borrowing so it doesn't go up in value but housing is restricted through zoning and the availability of land, you just can't make more of it.
You're correct, but the other thing with housing is that we actually have a supply glut. There are something like 16 million vacant homes in the US (according to numbers from an internet search).
Why so many vacant homes? The answer (as with everything in economics) is that the incentives are such that it's better to sit on a vacant home. In other words, our current system incentivizes hoarding homes.
This is false, "vacant homes" has no relation to "vacant homes you'd want to live in". Half could be condemned shacks in Detroit and the other half could be homes people have signed leases for but aren't moving in till next week.
And it's impossible to make squatting on a vacant home worthwhile, when you could be earning rent from it.
Making it easier to obtain leverage doesn't make housing cheaper, it just makes the prices go even higher faster.