Markets partially solved this problem a more than a century ago - the solution was "really shitty, cheap, shared housing". As a society we decided that such housing was unacceptable and banned it without providing a replacement.
"This enormously regulated industry doesn't yield outcomes we like for the poor! Obviously markets cannot solve this problem!" is a disturbingly common argument.
"This enormously regulated industry doesn't yield outcomes we like for the poor! Obviously markets cannot solve this problem!" is a disturbingly common argument.