Valid. This is a tragedy of the commons. The problem is they’re being used for the private benefit of those camping on them. That will eventually undermine support for funding them.
Yes, that's why you spend money on housing; for pennies on the police state dollar. Granting a person a room is a one-time cost, which can be diminished with larger builds, and a modest upkeep. The criminal justice system incurs significant ongoing costs per incarceree. Moreover, a criminal record is a barrier to employment, which tends to entrench people within the criminal justice system -- these costs can avoidably result in a lifetime of wasted taxpayer dollars.
Getting a person a room is, indeed, cheaper than running the whole criminal justice system if there had been such a person, giving a room to whom would stop all the homeless crime I'd be first to pay for their room my own personal money. What you meant, I believe, was running a free housing program for everyone, not a room for one person, right? And then the one-time cost is not one-time anymore, as people will be constantly demanding free housing, and modest upkeep is not so modest especially with larger build. And you still need to run the criminal justice system.
I am shooting in the dark here, but are you even aware of the various free housing programs that the US already had tried in the past[1]? Those did not solve the issues and the proponents blame them being too cheap on the failure.
I grew up a block away from housing projects in Seattle, where many of my friends lived growing up. They were recently demolished, the majority of their residents sent packing (hello, homeless population!) and the developers who were granted the land sold most of the houses at market rate. Yeah, I'm familiar with what's been tried.
When a halfassed attempt fails, do not conclude that a full and honest effort would also fail.
So if I got you right, you are saying that not enough money had been spent on the government housing (after insisting it will cost mere pittance to build and maintain)? These programs were not cheap already so whatever you propose should cost even more.