If people carrying guns in such situations tended to make them safer, what we'd expect to see is a statistical correlation between concealed carry and lower violent crime. But the correlation runs the other way:
https://www.theatlantic.com/politics/archive/2017/06/right-to-carry-gun-violence/531297/
Because guns put such huge emphasis on possession of the initiative, they have a tendency to turn non-deadly situations deadly. If you've got a gun on hand, you can't wait around until the other person makes a definitively violent move, or it's already too late for the gun to help. If, for example, some strange guy is rapidly approaching you, you only have a moment to draw and point that weapon if you want it to matter. But if you draw, and he has a gun, then he also is in a life-or-death situation where he has only a moment to draw and shoot. Or, if he doesn't have a gun, he has a second to move for yours in hopes of disarming you, potentially resulting in one of you getting shot. A misunderstanding that may not have actually been threatening at all can turn into a deadly one in just a moment.