I feel like we are killing ourselves trying to solve the “few bad breaks but totally capable of participating” type of homelessness so that we can ignore the “I will never fit into your society” type of homeless. The solutions for the latter are much harder, both morally and financially.
It’s also politically expedient. The right loves the “worthy homeless bootstrap story” and the left loves that you can blame that homelessness on failures of capitalism. Nobody likes involuntarily committing people to long term inpatient care at public expense.
Some people get a really bad dice roll. Ignoring that doesn’t make it go away. It isn’t fair and we like stuff to be fair.