its not a sloppery slope argument. imo, the slope is already slipped if you are claiming they can sleep anywhere just because they can't find a place to sleep.
your counter example is not quite there. I dont think anyone is saying they can't sleep in ALL public places, just that there are limitations on where they can sleep in public.
for instance, is it OK for you to park in front of a hospital in such a way that it blocks ambulances from entering? no.