Your argument falls flat once you remember that there is in fact plenty of homeless people and there will always be those who will choose not to pay irregardless of logic or desire of self preservation. And while yes, any privatization of housing isn’t really any good, but you don’t have to make it impossible for them to make money off of it. You just play their own logic against them and keep it just on the line where they will ultimately go for something else to profit off of other than housing as their returns and infinite growth will eventually lead them into microscopic margins so any variability becomes a threat to the bottom line.