Yep, One of the things I remember our instructors teaching us at the police academy is the deterrent value of "presence." If you're there and you look ready (and, frankly, armed) you can deter a whole lot of badness. In my Academy class there was a super-nice guy who was something like 6'9" and looked like a Serbian war criminal. No one wanted to screw around when that guy was nearby.There is no way to prove a counterfactual, but I will go ahead anyway since all those rules don't matter and the points are made up.
Police showing up to a "non-violent" call deters someone from getting more violent. Agitated, mentally ill or nefarious folks that are presented with some social workers talking about their feelings are going to include violent solutions in their calculus more often than they would if presented with armed LEOs. Change my mind.
I also saw something similar when I was in the Army. I think I mentioned this on the site before, but when I was a company commander in Korea, my first sergeant and I got regularly tagged for "presence patrol," which involved us going into all the "juicy bars" (i.e. bar/brothels) and other places frequented by US soldiers in the Uijongbu area. I deeply disliked this tasker, because 1) my soldiers were Korean linguists and didn't frequent those sorts of establishments because they could speak the language and would go to places that US soldiers didn't typically go., and 2) we had to be unarmed.
My first sergeant and I came out of one juicy joint near the train station and walked right into a standoff between a group of drunk GIs and some Filipino pimps armed with switchblades. Us being there gave the GIs a reason to back off and save face, and the Filipinos didn't want to fight because they were now badly outnumbered and outflanked. Good times.