Homelessness should be illegal, but for the state, not the Homeless. If your State is run so poorly that you have a significant number of Homeless, then you are committing a crime against the people that live there. You've let rent get higher than wages, you aren't adequately funding mental and physical Healthcare, you're under providing Unemployment benefits and Disability, you're not regulating unnecessary layoffs.
Are there going to be a few people who still choose Homelessness, maybe, but these are problems with solutions 99% of the time.