Let's be clear, you're arguing against data by waving your hands. Then using your "they're not from here" assertion to justify the city not dealing with the problem. Then suggesting that the Federal government should do this without talking about how that could possibly happen.
I'm pointing out that the demand for housing in any city is elastic; if you house the current 6,000 homeless without addressing the systemic problems, more arrive to take their place and you're back where you started.
Rich European countries which have solved this problem don't do it by putting all the homeless in Paris or Berlin. They're distributed throughout urban, suburban, and rural areas of the country, which is what we need to do.
It sounds like you haven't really gotten to know many homeless people. If you did, you'd realize that what they typically need is not a job but something more like basic income - food and shelter, which can be more easily provided in a place that's not the most expensive city in America.
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.
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.
What end game are you trying to get at?