I think the idea that we are not trained to handle guns comes into play here. Does a basic know how to intubate through practicing on the dummies at the station? Maybe, does that mean they can safely do it in the field? Possibly, does that mean they should? Not likely.
I have grown up around guns, I can clear probably 99% of the guns you will find in the public without hesitating to figure it out. But while on duty as a paramedic/emt/ambulance driver, that is not in your job description.
In my opinion after speaking to a few different cops who have POST certs, they recommend leaving in place, calling enroute to hospital and the police officer removing the weapon prior to bringing into the hospital.
Most CCW are holstered and so sometimes better left in place, and if we have to remove for patient care, they suggested if police were not on scene or in the unit, to remove the holster as a whole and lock in the lock box.
What you have to do is think almost worst case scenario. Yes this person is hurt, but was this gun used in a crime? If so, chain of custody plays a big role in what you do with the weapon.