In your situation that makes tons of sense considering that you are the only full time emergency service around besides a sheriffs department or something. I'm sure they too are stretched very thin, and have no interest in rescue services. But for areas that have 24/7 FD coverage with good staffing and equipment, wouldn't it make sense to save more ambulances for EMS calls?
Yep, if the FD is performing the job well then why not. My point all along has been you can't apply the "FD should do it" model everywhere, and that extrication at its core is a patient focused medical activity and just because someone has rank doesn't mean they should be making the decisions.