If you want to see what cheap housing and food without economic opportunity go to rural West Virginia. It doesn't work well. The first steps you describe need to be followed by incorporating people back into the economy.
The natural tendency of a competitive (capitalist) economy is to exclude a subset of people. The "economy" is the cause of homelessness, not the solution. The solution has to come from outside the economy.
Economics is how we allocate scarce resources. Outside the economy is where people go when their theory needs to ignore how shit works.
My meaning was outside the capitalist system of exchanging services for goods. Many, many people need goods and have no meaningful services to exchange. The idea that we need to cram all of these people in the most dense and expensive centers of capitalist activity is ludicrous and harmful.