I have no idea how police are trained but it seems situational awareness and decision making is something they should spend more time on.
Apparently police officers spend 58 hours learning how to shoot, but only 8 hours are spent on de-escalation tactics.
I'm British .. we have pretty much the exact opposite of what you describe - we arm our officers with their mouths, and have firearms teams that can be called in if required. I guess this makes me biased, but I do see asking an autistic patient (especially someone severe enough to need to be homed) "what's wrong?" to be more intuitive than firing at them.
Missing and hitting someone else just has to be the icing on the cake.
What you describe for your British officers is training, which we apparently don't have. But I have to ask, if these officers encounter a situation they believe is a violent escalation do they just starting talking right away and handle the whole thing themselves? Or do they engage until a specialist is present, such as a hostage negotiator? If they do, then that's identifying and containing the situation until it can be resolved. That was missing from this situation.
This is whats happened in the US.