From my experience, homelessness is not affected by police presence/enforcement other than to force them into other areas. An unhoused person has to go somewhere, so using police to approach that simply pushes them in larger numbers into other areas, making it someone else's problem. That seems like a huge waste of resources.
There’s a sick irony that the very same people who are fighting “for” the police against the defund crowd also demand police officers perform tons of unnecessary grueling work the police themselves willingly admit they aren’t trained to handle.
I think for many people “Support the Police” really means only support their budget; not support them as human beings or public servants.
So much of what you said is, honestly, what a lot of homeless people need to do, just to survive. When you don't have safe, ready access to bathrooms, you go outside. When you don't have a job and can't get money, you steal to eat. When you are subject to this misery for long enough, you stop caring about what polite society cares about.
Police presence sure does deter this behaviour, but only where police are present. It doesn't _stop_ this behaviour, because it can't. Cops can't fix homelessness, they can only move it along somewhere else, turn it into some other neighborhood's problem.
If you really want to fix the problem, look at you and me. We don't crap outside, we don't steal, we're not making neighborhoods scary and dangerous (I assume). And why? Because our basic needs are met. We have food, water, shelter, sanitation, entertainment, employment. If you really want to fix the problem, THAT'S the problem you fix. Sadly, social programs for the homeless ("handouts") aren't nearly so politically popular as spending that money on policing, the legal system, and the prison system, despite being many orders more efficient.
It's these people that need the strong hand of law enforcement to whip them into shape. It's for their own good, honestly, which bothers me as a big proponent of personal liberty and personal responsibility. But their options are either shape up, or slowly decline to a tragic death. A puppy who is not trained not to bite toddlers very well may end up getting euthanized. Sometimes strict enforcement is the morally just choice.
edit: my point is that both are needed. The options for the self motivated, and the guiding hand of arrest for those who cannot save themselves.