So she gets angry with Penguin's comments. Last time I checked, emotions weren't illegal.
Actually, I was referring to Batman.
In our world, your argument is entirely sensible. However, the GCPD makes uses of Batman's services in this very arc and in much the same way as Batman is doing here, so I think it's a little disingenuous.
Batman doesn't use weapons against good police, Batman doesn't fight good police, and the MCU knows that perfectly well.