Almost all homeless have mental illness and/or substance abuse issues. That's why they are unable to act on one of the endless options that exist at the moment that can get them even the most basic of accommodations and employment. The people your solution truly helps are the non-homeless poor. To be honest this is a much easier issue to address given some willpower. Then again, as a Canadian, I find basic medical care to be a no brainier as well, which seems to be something the US struggles with quite a bit.

You can't simply suggest that addiction/mental illness is "self inflicted", give them $10K and say "You're on your own, bud." That isn't solving anything. Solving homeless is the same as solving mental illness and/or addiction, and those are massively hard problems to address.