twobravo,
Yep, worked as a volunteer in KCMO metro area for 8 years. Almost all the departments in that area (and likewise around Tulsa) have either pumpers with EMT-Bs that respond as first responders to med calls, or a "squad" or Q/R (ours looked just like the Squad 51 from the old "Emergency 51" TV show!), but separate "contract" ambulance services that do the transports. In the suburban and rural areas, it's not uncommon for the FD to get there considerably before the ambulance, so they do a lot of "stabilize and package" and have the patient ready to go when the ambulance gets there.
In those (rural) cases transport is a problem, because while the volume of calls is relatively low, a couple of ambulances can be "posted" to an area, and respond to calls for several suburban departments. If they'd tried to run their own, their ambulance would be out of district for an hour or more by the time the run to the hospital, clean, restock, and then drive (non-emergency) back to their post. Much better to have the regional contractor just start an in-service bus from "downtown" our way when the one out on our call starts to the hospital. It spreads the ambulances thin, and increases response times, but requires less hardware. That works because the FDs with the first reponse duty don't have the long response times.
This model breaks down somewhat in the city itself, though. Generally, there are a high enough volume of calls in the city center that (no matter how spread out the Posts) there is always a bus available. This means that the ambulance frequently beats (or ties) the FD to the scene. That gets frustrating for the pumper crews (get there just to watch the ambulance drive away, or cancel them) but is nice for the ambulance when they need "more hands". In the city, moving the ambulances to direct control of the FD changes very little (but messes up the rural areas that depend on the city's support to provide the hardware!). But what it does do is set up turf wars between the FF's that run the bus, vs the FFs that ride the trucks.
So that's the trade off - do you have FFs w/EMT training that do First Response, and separate ambulance service, and then have turf wars between the FD and EMS service? Or do you have FF/EMT first responders on the pumpers, and OTHER FF/EMTs on the ambulances and have turf wars between the guys on the bus (that want to be on the truck) and guys that want to be on the bus and resent the extra training they have to go through to fight fires?
Catch-22!