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.