Well I guess where you are from that is an option. Not here in the metro Atlanta area. You are either a firefighter/paramedic or you don't have a job.
But the patient care scenario is easy to answer. When I am on a medical call the patient is my ONLY priority, with the exception of crew safety. When I'm on a fire call I engage in firefighting only after evacuating and/or treating any patient found. Patient care is still my #1 priority, on a fire scene, car accident, haz-mat, whatever, it's in our SOP's for medic's. All of the other functions (firefighting, extrication, etc.) are handled by FF/EMT's.
I find no reason to go "search out" an only EMS organization in my area. If I thought my dept. had poor patient care standards I would leave in a heartbeat.