We do actually spend a lot of money to "help" poor people in various ways, we're just allergic to giving them cash. Maybe food stamps (which is a close second to cash, admittedly, we just don't give people very much), maybe some housing assistance of some sort, but we just can't bring ourselves to give people cash. That's what they need.
If we're going to do the paternalistic version, which is that we can't give you cash because we need to make sure you make the right life choices instead of spending it all on T-Bones and Cadillacs, then we have to do that better. Doing it right is really expensive, by having case workers with actual resources really working with families.
I guess those homeless kids just need a bit of gumption.