[bunderbunder]

I wouldn't at all be surprised if it's far more common for police getting jumpy to result in physical harm to hostages than police being cautious and prudent does.

The whole point of taking hostages is to try and slow the cops down, and get yourself some leverage in negotiation. If the police are acting in a way that makes it seem like that's not going to work, then the hostage-taker will stop seeing those people as being useful as hostages, and start making decisions accordingly.