Ok, since we're going into the fire-based EMS/EMS based fire suppression debate, I'll chime in anyways (I didn't want to be the one to switch the tracks).
Is it really cost effective to have medic engines? First, as was an incident around the new year in Philly where a patient died waiting for over an hour for an ambulance, fire engines normally can't transport patients.
Even the ones configured to be able to transport seem like they would be a complete pain to use for transport. So, even if you are using the fire department to run EMS, someone is still going to have to run ambulances.
Now you have another problem. If you have an paramedic engine on a medical call, then the engine is not available for a fire. Similarly, if you have a medic engine on a fire call, it isn't available to run EMS calls. Yes, it is cheaper to put medics onto fire engines than increase the number of ambulances. Unfortunately, it doesn't really solve the problem of an over taxed EMS system, just makes the numbers look better (afterall, who cares if that heart attack is sitting on-scene for 20 minutes waiting for an ambulance if the first responders arrive in 6 minutes? Sure, you've met the response time goal, but the patient isn't significantly better for it compared to if there were more ambulances).
Furthermore, I don't buy the synergy argument (i.e. what about patients from fires/hazmat/that require extraction). Interdepartment training and planning at the executive level should solve most of that. Most patients don't require the services of traditional fire department roles (rescue/fire suppression/hazmat), so it is a non-sequitur.
Finally, there's the problem with willingness. Are their fire medics who are great fire fighters and paramedics? Sure. Now, how many fire medics out there would be happy if they never ran another medical call in their entire life. You simply can't expect these individuals to keep current and improve themselves in fields that don't interest them. It's not necessarily bad or wrong, as long as your job doesn't depend on it (example: I couldn't care less about fire fighting techniques, research, operations, etc, but I'm not a fire fighter nor do I want to be one. If I did, I would care).
Of course this is why the IAFC is opposing requiring better standards (such as degrees) for paramedics [page 3] [PDF file]. I would imagine that an EMS based fire suppression set up where the goal of the agency is EMS first, fire suppression second, would have piss poor fire fighters for the exact same reason that fire department has piss poor medics.
As far as paramilitary style vs more relaxed style of management, I don't think there needs to be a rank structure in medicine. Hospital personal seem to get along just fine without having a captain and seem to be able to build patient care teams comprising of numerous physicians, nurses, and other allied health providers without captains and lieutenant, epaulets or badges. Most ambulances have 2 providers on it. Is there really a need to have someone be a commander of 1? What about situations where the higher ranked individual is of a lower medical qualification (I do have a story about this actually)? Maybe it's more understandable when numerous people in different locations need to be coordinated or controlled, but I don't see that happening often in EMS.