In NYC, a lot of the affordable housing stock are part of co-ops, where the board has to approve your finances before you can move forward with a purchase. If your monthly income is less than a certain multiple (you would think 3x, but it's usually 5x - 10x depending on the co-op) of your monthly payments ie maintenance + mortgage + insurance, they can reject your application.

And even if you found a condo (usually 2x as expensive as a co-op for same QoL) without a board to reject you or just lived in a city without co-ops holding a lot of housing stock, banks have similar requirements in co-op applications as well. So you really need to have a massive income to go in without a >20% down.

Among the young people who may like to buy a house, this probably applies to a few rare folks working for a bay area tech company salary but are allowed to live in any other city where the home prices are more affordable.