> a larger part of that concern is people worrying that somebody else is getting something for free when they have to pay for it
There are plenty of examples of politicians making promises of spending now on others in order to gain cost savings down the road. Obamacare was sold to the all-too-eager masses this way. Especially at the county/local level, such cost savings arguments could be made very effectively if there were convincing numbers to back them up. You could also make arguments that public health and land values could benefit from such spending. I'm basically sold purely on a public health argument.
What I take issue with is your abstract line of thinking. First, those who oppose you may not be as shallow (nor ignorant) as you seem to suggest. For example, I would love to see temporary housing, drug treatment, mental health counseling, and job/life-skills counseling to be setup for the homeless. But my local government is so disconnected from reality and are so wholly lacking in priorities that there would never be enough political will to allocate additional budget enough to truly address the problem. So, I oppose you on budget priorities grounds: politicians need to make eliminating homelessness a priority at the expense of some other program - and they could care less about the homeless. The taxes are already too high, and there's a laundry list of bullcrap that the city and county does that could be cut in favor of actually helping those who are in real dire straits.
Second, the environment into which the homeless enter is not a vacuum, and at least local to me, the government had a big hand in creating the current homeless crisis we see (legalized building structures for public overnight camping in the streets.) Coupled with our generous social services that keep people alive, our already bad homelessness problem has metastasized into real human tragedy. So, while I am pained to see what's going on here, I am also deeply skeptical that there is enough wisdom in my local officials to deal with this problem when they were fools at the start and caused it to flare so badly. I oppose you in your thinking that government is capable of solving this problem.
Third, the opinion that additional public services for the homeless become an incentive to remain homeless is a legitimate one regardless of how crisis/fear-minded you are on the subject. The crux of my argument is that dependency robs people of their liberty. The systems we have today for supporting the homeless create dependency and are unjust for that reason. I am in favor of increasing services, housing, and even outright paying people who are homeless to get them out of their situation -- BUT, to get around the dependency issue, there needs to be mandatory work. We need to create a more comfortable life for these people and provide a real possibility to emerge and be self-sustaining. And, at the same time, it has to be UNcomfortable because we expect work out of them. I oppose pure charity to otherwise able-bodied people if that charity will keep those people in their miserable place.
If I were el presidente benevolent dictator, I would make homelessness illegal tomorrow. Along with housing, counseling, and rehab, I would give people who break my law a choice of a few kinds of make-work while they sort their lives out. If they are intractable or fail to show up for their new job, they get sent to the work farm (essentially forced work prison where they get paid real wages) or the military if they are fit enough. For people unable/too sick or those not in their right mind, I would reserve the biggest cash outlays in order to provide comprehensive care for them.