A 20% down payment requirement is certainly reasonable but not if the government makes the requirement. The government is incompetent and/or destructive when it interferes in the market.
I'm fine with the free market determining the terms for loans if the lender eats any losses rather than selling the loans to Freddie/Fannie or coming to the taxpayer for a bailout.
It's because we have not yet thoroughly purged the idea of "too big to fail" from our culture that we have the government setting these requirements.