Every near miss I have had in a crosswalk has been a cop car. Every one. No sirens, no emergency, but you can be halfway across the street going into their path and they don’t even slow down.
Most I have ever personally pissed off a cop was the one stuck behind me in a school zone… And I wasn’t taking any chances. First opportunity, he peeled out around me and took off (again, no siren… Otherwise I would have pulled over out of the way).