We bought a fixer upper (borderline tear-down) for roughly 2x my income at the time (and then sold it for 2x after 5 years after fixing it up). But just for argument's sake, let's say you buy a house (or apartment) for $400k, which you can absolutely do in DC (for example):

https://www.zillow.com/homes/for_sale/?searchQueryState=%7B%... (hopefully that abysmal URL still works for you).

$400,000 x 3.5% = $14,000. If you can't save a $14k down payment, you probably can't afford the mortgage on that and the associated upkeep anyway.

Don't get me wrong, I'm not defending the housing market. I just wanted to point out the FHA program since it helped me, personally.