When Merete Muenter tells people that she pays $623 a month for her studio in an affordable housing complex in New York City, many assume the worst: a run-down dump in a crime-ridden neighborhood. The reality is that her subsidized rental is far nicer than any of the market-rate places she’s lived in previously. “People … don’t realize that my affordable housing apartment is in a luxury building that has all the amenities that I never dreamed of having, living in midtown Manhattan,” says Muenter. “I have a doorman, elevators, gym, roof terrace, courtyard, even a washer and dryer in...