These are the factors that make me think higher down payments would be beneficial. Specifically, they would lead to lower prices and cool the over-heated market, which would reduce opportunities for runaway speculation.
I happen to believe prices are unsustainable now, as they were in 2006-7. I'm actually surprised prices didn't fall farther and stay there longer back then. When working stiffs can't afford a home, something has to give. The best way to make homes affordable is through lower prices, not by making it easier to borrow enough money for higher prices.
Obviously, there are a vested interests in keeping prices up, keeping buyers borrowing beyond their means, and keeping speculators speculating.