Yes, there are some synergies with having FF-based EMS. The personnel are already cross-trained (I say trained for a reason) and much of what they do is related (MVAs require FD for rescue, in most communities where EMS doesn't have "organic" rescue expertise, for example), and the stations are already there. However, remember that most of what the FDs do today is superfluous -- the reason why we don't have lots of fires (or lots of folks dying due to fires) has nothing to do with fire departments, but everything to do with engineering and fire protection technologies. Better construction has reduced the need for fire suppression and financial innovation covers the risk from the cost side. Fire departments are -- on the mean -- overstaffed and overfunded.
Some of the cost disadvantages of FD-based EMS:
-- You're pulling out engines and ladder trucks -- it costs more to have the 3 FFs and 1 officer on an engine respond than it does an EMT/Medic ambulance, and the value-added by the FF/EMTs is pretty minimal, other than for lifting. And we can easily substitute capital for labor (think power stretchers), which are much cheaper than (unionized) FFs. If you really feel that we need more personnel at any given call, I'd wager that the costs (fixed and variable) for having a 3 or 4 person-staffed ambulance (or 2 person ambulance with a 1 person fly-car) are dwarfed by a fire engine.
-- FFs don't want to be doing EMS, on the mean. Less motivation can quickly turn to lower quality of care (or, at the very least, not up-to-date care because of a lack of engagement with the literature, etc.)
-- It provides a reason to add staffing to fire departments where the marginal benefits are exceeded by the marginal costs (i.e. the value added of another FF is smaller than the added benefits provided).
I like to think of FF-based EMS as well-intentioned (even though it perpetuates an extent and outdated system) but ill-informed. Firefighters don't fight fires. We are better off having single-role EMS personnel do EMS, not firefighters.
When there is a fire it is very labor intensive, yes today there are more EMS calls than fire, but a fire takes longer than an EMS run and requires a lot more people to put it out.