In the United States, if you look at the homeless people, then you will find that for most of them the condition was caused as a result of drug addiction, gambling, mental illness.etc. The government can't do much in these cases.
Can't or won't? In the US there are entire neighborhoods where people live in trailers. it is the richest country!!! I think that people need to educate financial literacy, and it is in the power of the state.Homeless is a lifestyle. No one can make me live at home and be sober! 
In most cases, they can't because people choose to live the way they do, whether they choose to do drugs, join a gang, or just decide they won't work. Also, yes, the US might be the righest country but we're also a very broad and varied country. You just can't compare inner-city Chicago to the California Hills.