It might make sense to combine the firefighters and paramedics into one department as skills overlap in many areas. Obviously we would still want to still send a fire truck with the ambulance in medical situations for reasons discussed above. Then you would need specialization between firefighters and the EMTs but they would complement each other in most situations.
I’m in Southern California, where we have just about every imaginable permutation of emergency medical care. I’m pretty fond of the dual function firefighter/paramedic concept. When a city reaches a size where every station has a staffed paramedic ambulance, I don’t mind them running Basic Life Support calls alone.