Certainly there are pros and cons to a split system. On the one hand the ffmedic would get back to the action faster if they turn over care. On the other hand can they guarantee continuity of care for their patient. Yes, on paper a medic is a medic, however, we have all seen paper medics. FF/ medics in all area are held to a higher standard they everyone else. They do not ride the lazy boy or hang out in the gym all day. when they are not on a call they train and train and then they train some more. We are still the Johnny and Roy of old who perform on multiple levels am do it well. As for the money side of it, municipalities that bill patients do so under the same guided lines as private care companies including the handling of medicare and medicaid. The bottom line is that 80% of fire calls are EMS related and the departments should be capitalizing resources that direction while maintaining a fire ready status. Keep in mind they are only running 911, they are not running the other 98% of the private calls like interfacility transports, dialysis runs, and clinic visits. I have been in the system for 30 years so I have seen it all, don't be afraid AMR be happy you can now dedicate to the other 98%.
I agree that in an ideal situation, the first-in medic should continue care during txp. However, it's a detriment to staffing if your only medics exist on the suppression apparatus. It's unreasonable to give up the engine medic for every patient needing ALS. If a fire department insists on providing the best patient care, and providing tx/txp in a timely fashion, the department will staff their ambulance with either one or two paramedics, preferably single role. In an EMS system where every employee is an employee of that jurisdiction, they're all held to the same training standards. There should be a system in place to properly give report and hand off the patient. In that case, the second (transport) medic is perfectly capable of continuing care without any hiccups. The transporting medics will likely be working with the same fire crews, so transfer of care should be smooth.
The problem is when you have only firemedics on apparatus, and a private agency transporting, because the hiring standards and training are inconsistent, and the average tenure of their employees are typically short (generally newer, inexperienced medics). I've worked for several privates, and the training is typically poor. You may get a brief inservice for a new procedure or piece of equipment, and this typically occurs on a different day, not while on shift. Their days are spent running constant calls.
I find it hard to believe that the firemedics "train train train" all day in EMS when not on a call. I'm a firemedic. We get 8 hour continuing ed. three times a year, on duty and OOS, quarterly on-line training, and some occasional in-station drills, probably for an hour or two twice a month. That's probably more training than most privates, and probably the same amount of training that a third service does. This is a department that is is training-intensive. Firemedics are no more proficient than a third service or hospital based medic. If anything, the firemedic has more job security, so the QA/QI is more lenient, and the testing can be less strict as well.
If anything, the firemedic has to devote equal time to suppression training. This isn't too difficult to do, so long as you actually devote at least an hour to training in either fire or EMS every day (not including a street drill). From experience, I can say that wearing multiple hats becomes very difficult when you add additional specialties, such as TROT, Hazmat, and Heavy Rescue Squad training. There's just too much training to be good at three or four things.
The above all relies on the firemedic taking EMS seriously, and not as a necessary evil in order to do fire. I find that our most proficient medics are those that started in single role EMS and escaped to fire, or those that joined the FD because there's no other good EMS employers where they live. I also see firemedics that truly enjoy EMS initially, but grow to resent it years later because they keep getting detailed to an ambulance when they would prefer equal time on a fire piece. That would somewhat describe me. We spend most of our time running BLS, so I tend to become disinterested in EMS (not outright resentment - yet), and this results in doing less training and reading about emergency medicine. It takes a good tour or two of good ALS calls to renew my interest in EMS. Understand that I started EMS in NYC, where an upgrade to ALS means that you see mostly ALS patients, and you aren't dispatched to any BLS calls. That was an important benefit to going ALS - way less "nothing" calls. Now, that's 80-90% of my call volume. Recently, though, I had a V-tach with a pulse, a respiratory arrest, and two patients with agitated delerium where I got orders for ketamine and versed. I might not see that degree of action again for three or four months.
All-ALS transport systems (fire or single role) suck for that reason, IMO. Also, realize that single role medics typically burn out in 7-10 years on the average, so the problem of becoming disinterested in EMS after some years is not specific to the fire service, not in the least. I have 12 years in EMS, with at least full time hours on an ambulance, so I can vouch for the 7-10 year estimate for burnout. If I was still sitting on street corners doing EMS in NYC, I would be burnt as well.