Homelessness isn’t really caused by housing prices, people just move to worse places or get roommates. Crime definitely isn’t caused by housing prices, it’s plunged as housing prices have soared over the past 30 years
I don't agree with your assertion that homelessness isn't caused in part by house prices. That seems unintuitive to me. Yes some people will get roommates, but what about people that already had roommates and were barely meeting rent? Some of them will have the foresight to get up and move interstate before they get wiped out, but there's frictions and costs associated and not everyone will succeed.