In my area, unless the officer is so inclined to keep up with skills on his own, the first responder class s/he had in class will be the last time they are taught anything more advanced that first aid and CPR/AED. This doesn't exactly compell them to be involved in our jobs. I'm not saying that they're not helpful overall, it's just that some of the new officers are not excited to jump into a medical/trauma emergency. The ones that do help do so because we have a very good relationship with our LEO's.
As far as safety is concerned, (spenac jumped on the soap box before I got a chance ), I remember reading somewhere that emergency response coming from different directions is a significant cause of accidents in emergency response. This may be a factor in their decision to run without L/S and give the right of way to EMS. In my area, LE response has typically been with the use of L/S if appropriate based on the call. I'd rather have a LEO =-respond non-emergent than hurry up to get there and not be helpful. If nothing else, we've had a few of them drive. They find out how spoiled they are with the Chargers.