> She was unarmed, in a group of people who all looked unarmed in the video. None of them was holding a weapon
There are no firearms visible in the mob in the video; there are weapons in active use in the video (against the barricades, but if you are responsible for protection of life you can't assume that that will be abandoned once the barricade is down).
> much less training it on the police.
The police aren't the main people that the police were protecting. (That some of them were acting as literal human shields at the barricades makes that clear.)
What would you have had them do? Allow a breakthrough, reassess the intention of the mob, and if it was still an active threat start firing then, without the passive defense of th barrier? As well as endangering the lives they ought to be protecting most urgently (the ones not engaging in a violent crime), and their own lives, unless the crowd instantly became pacific after breaking through the barricade, that would have resulted in a whole lot more dead insurrectionists, because there would be no choice but to fire as fast as aim can be switched to a new target until the crowd stopped.