>>If instead you mean police should respond swiftly but not bring out the SWAT teams without more verification, then that could pose a (different kind of) safety issue for responders and potential hostages.

I think you're getting close to someone people don't like to talk about; we (as a society) seem to value the lives of police officers far higher than we value the lives of innocent "civilians". This seems entirely backwards to me - I'd strongly prefer that police officers effectively never fire first. Let the SWAT teams be very highly armoured and lightly (or non-lethally) armed.