"I witnessed a San Francisco police officer telling a group of homeless people to move on but having no answer when asked where they could move to"
As I said, I witness this extremely regularly just outside of my apartment. It ranges from a patrol car stopping for a few minutes to just give a talk to the homeless people that amounts to "hey, we're the police, we are letting you know we're here and we've got our eye on you... we know you can't magically stop being homeless but please stop looking so homeless", all the way to 4-5 cars + a firetruck/ambulance on standby while the officers make the homeless people take down camp, pat them down, etc. with sometimes a city sanitation pickup truck taking away all of their possessions as garbage (it seems that many homeless people are hoarders).
I'm not sure what's going on "behind the scenes" here. Is it an irate neighbor that calls the police complaining about the homeless people and asking them to do something about it, which they then do their best to? Or is interacting with the homeless population an actual, documented part of their job? If so, is it tracked? What are the outcomes they hope for?
What I observe is that when they make the homeless people leave, they'll typically be back a few days/weeks later, so clearly this is only shuffling the problem around, rather than actually solving it in any meaningful way.
My hunch is that this is all essentially theater - the police/fire department know they can't do anything, but have instructions from above to do "something" about it, so they just end up doing what they can, even if it is utterly pointless and ineffective. But at least the irate neighbor is satisfied that there are no more homeless people outside their window for now.
It's all very sad.