I'm totally against sending unarmed people into an active scene.
That said, if, perhaps, you're a small community, with limited LE response available, and a full-time paid fire department that does EMS ( for the reasons that @TGS stated) that this might work for you-IF the agencies involved are all in and willing to spend the training time and money.
Fire department because you aren't going to want to take providers off of ambulances to do this. If anything you'll be drafting people to drive the ambulances so the (normally) 2 person crew can both be in the back treating the patient(s). (Echoing @Nephrology 's point)
I work in a large urban area. I have never once been on a violent scene and thought 'there aren't enough cops here'. It makes more sense to me to let the responders who already have the skills, equipment, and experience to move through hot scenes to do that.