I would assume, rightfully or wrongfully that a society in which police do NOT have guns would generally be a society with less gun violence. Just an assumption that if police don't carry guns it means they don't believe they will be dealing with many others who carry guns.
Police may carry fewer guns when they believe that they won't be dealing with many others who carry guns but I doubt that.
First off, if the police carry fewer guns that doesn't change the reality that many others carry guns. The two ideas cannot be scientifically or statistically related. There could be a cause and effect of fewer bad guys carrying guns so the police choose to carry fewer guns but there would be absolutely zero cause and effect of the police carrying less guns so the bad guys carry less guns.
And what the police "believe" can certainly not change the number of bad guys carrying guns. The human mind is not yet advanced enough that they can control the behavior of others by thought - especially by remote thought.
Of the police are smart, and I believe they mostly are, they won't quit carrying guns as long as they think there is a chance of dealing with even one, single, person carrying a gun. I know I won't quit carrying one even then.
I'm not planning on a fair fight in self-defense; I'm planning on surviving a fight of self defense. For me, I will carry a gun as long as I believe there is anyone who might choose to do me harm, even if only by biting me. I might not shoot someone for biting me but it's always on the table. Why would the police take any different stance on their lives?
In fact, if someone fights with a cop, takes a swing, wrestles with them, pushes them, in any way gets into a physical confrontation, the cop should use his gun and shoot to stop the attacker; they should assume that if someone is attacking an armed cop that their intention is to get the gun, shoot the cop, and then shoot others.
This one turned out OK for the cop:
A California man threatened to shoot a police officer "right now" as the two men desperately grappled for control of a gun during a violent altercation Sunday that was caught on the cop's bodycam, police officials said.
www.foxnews.com
This one didn't turn out well for the cops:
Avondale, AZ – An Arizona Deputy of Public Safety (DPS) trooper was fatally shot, and another was seriously wounded Wednesday night. A third trooper was also injured in the altercation. “The DPS family is in mourning. Our thoughts and prayers are with his family. Lives have been shattered and...
policetribune.com
Yes, cops, just like any one else, should be armed to defend themselves and, if attacked, should defend themselves.