De-escalation is not what police are trained to do against active shooters. Quite the opposite in fact. Anybody remember the Columbine shootings? That was a de-escalation. It did not work out very well. A lot of things changed afterwards.
Once the bullets start to fly, the negotiations are done.
You’re right. If the robbers start shooting take cover. You should have already cleared any civilians out of the area. So there is no significant risk to non participants in this drama. Then you have a choice, engage the suspect in gunfire or wait it out. Engaging means almost certainly hitting and wounding the hostage - this is real life not the movies where a single handed snap shot with a pistol at 100 yards knocks the gun out of the bar guy’s hand. Or you can wait. Yes, bad guys may make good on their threat to hurt the hostage, or they may not. Your choice comes down to a couple of options. One will get the hostage hurt or killed, the other may get the hostage hurt or killed. Of course one let’s you be aggressive and take control of the situation, the other requires patience and letting the suspect determine what happens next. So we can all see how this decision comes out 9 out of 10 times. ...
Well... they’d stop taking hostages if the police were armed with RPGs.