>(how cautious varies from police department to police department, as well as far more care taken by EMTs)

In my experience police cars will turn on their sirens as they enter an intersection without slowing down at all, even though they didn't have them on in the first place any immediately turn them off afterwards, because they think that's legal and if it's legal there's no reason not to do it. Kind of surprising I've never seen one get T-boned.

Also in my experience ambulances do not do that.