Had you meant 3% + 1% PMI + 4% interest for an FHA consume 100% on median, because that definitely implies either high prices on houses or low median incomes.
I think this is a sad step backwards in the development of human society. It's downright dystopian.
The average household should be able to own an average home (or condo/apartment, for cities). For the same reason that the average person should be able to own a toothbrush, cell phone, some clothing, and so on.
This idea that it's just 100% OK that no real person could/should ever afford any housing, and every poor-middle-class person should always be beholden to renting from a private for-profit corporation forever is incredibly destructive to public finances and the ability of regular people to generate any meaningful savings or financial stability.