California

The catch is that

1. A smaller downpayment means a bigger loan, which means to total price of the home over the lifetime of the loan is higher.
2. It increases the risk that the owner will default on the home, since having sufficient savings for a downpayment is a good indicator of having the financial means to keep making payments.
3. Any time you use a financial strategy to expand homebuying power to more people, what happens is that more people can buy homes. If the market is limited in the number of homes that exist and can be produced, that drives prices up.

The math is simple. If you want more people to have homes, you need to build more homes.