" You may also say the roots of homelessness lie in liberal values."
LOL - no. Liberal values include state housing which is proven time and time again to end mass homelessness at a smaller cost than the law enforcement, judicial and social cost of managing homeless populations. Liberal values strongly support taking from the rich to support the poor, including the mentally ill and homeless. You do not see many liberal values at play here.
Conservative values of "everyone must work, no work means you get no pay, no pay means you have no home" is the core cause of modern homelessness.
Not everyone in our society will or can work, and those who don't are lucky enough to be supported privately or publically or they're eventually homeless. This is the reality of a conservative value system.
Also, it's not just mental illness, homeless and mental illness are not synonyms. Many people are homeless, living in cars, couch surfing, and are not mentally ill requiring institutionalization.