We're at a philosophical crossroads. We used to warehouse such people in institutions until we became "enlightened" by keeping such people out and about in society...arguing from the standpoint of compassion.
Well, ya gotta pick your poison. I've got a friend from high school who is mentally ill. (schizophrenic) It's been a combination of highs, lows, intreatment, outtreatment, alcoholism, multiple OWIs, and homelessness. Meds work for a while and all is going well until it isn't going well. The voices in his head are pretty convincing and inebriation is something he can't quit turning to in order to squelch the voices.
There most certainly is a case for busting such encampments in that the more comfortable people become, the less likely they are to seek treatment and try to change their lives. In addition, if you keep them moving they certainly aren't causing problems in your back yard.
A place like St. Paul can certainly make the argument that the situation they provide is cheaper, but only cheaper to the point in which it doesn't encourage a disproportionate number of people to go there. It's not cheaper if everyone ships people to such places and dump them off, but it certainly would be cheaper for Ames. They like Ames have the benefit that winter serves as a pretty decent deterrent...something you don't see in places like San Francisco, etc.
In cities like Ames all across the country which have stringent zoning and occupancy requirements for property owners, they shouldn't look the other way when such encampments spring up. It's an insult to taxpayers and other members of the community who are required to follow such laws. Unfortunately, the best answers are those which too many would deem as cruel.