No doubt there is substantial overlap between thieves / violent criminals and the homeless, but I’m not sure the bulk of the criminals are homeless. I’d also point out that often the homeless are the most likely to step in to help when needed - while people who’re busy going about their lives will often succumb to the bystander effect and continue going wherever they’re going.

I’d want to focus enforcement on criminals (homeless or otherwise) and people who are a danger to public health rather than the homeless in general.