Exactly this. I spent decades as a FF/EMT and that's the way it was typically done.
I did however, often carry a Baofeng programmed with _all_ the services with which I was likely to interact as a backup: MedEvac, EMS, law enforcement and fire services. Yes, I am a licensed ham operator.
The problem is there is no national emergency interop frequency plan, each state, county and city does things differently.
