Can't find a good job to afford a place to live? Good luck finding a good job once you have a criminal record.
The only thing the police can do is put them in jail. There are cheaper approaches to housing the homeless.
Not true, it gives them the ability to remove them from a situation and deposit them somewhere more appropriate for their needs.
Is it for the public good when it only benefits one group, namely the non-homeless? Because if police could arrest them, it would benefit you, but the homeless is getting a criminal record which would not only not benefit them, it would make their case even worse.