The general risk assessment is that medical personal don't know as much about firearms as Law enforcement - and LEOs don't know much. And you generally have other things to do that are more important than causing a negligent discharge in the ER.

Beside, do you really want to trust the Triage Nurse with a loaded firearm?

Medical staff arn't trained with guns and they figure there's less possibility of an accidental discharge the less people are touching it

Couple reasons.

One: do you know anything about that model of firearm? Does it have a safety? Can it slam-fire if handled improperly?

Two: Is there important information that can be conveyed by the present condition of the firearm. Was it a shooting or an accident. Would clearing the firearm remove important information that can be used to ascertain what happened?

Three: Preserving the firearm can preserve evidence. While that is not necessarily part of the duty of medical staff, there's no reason to risk destroying evidence if the firearm can be safely isolated with minimal disturbance.

Four: Why do it? An isolated, secure gun isn't going to decide to start blasting people on its own. What advantage is there to handling the gun more than is necessary in that situation? Get it out of the way and keep working.

Most modern handguns do not have a (manually operated) safety.

"A" is the answer closest to "remove all of the ammunition".