I'm sure you would love the Howard County (Maryland) Department of Fire and Rescue Services. They don't see EMS as an add-on skill. At HCFR, EMS (at the EMT-B level) is something that every firefighter is taught as part of the academy training. It isn't an add-on, it's a core component just as much as where to aim the hose or how to crib a crashed car.
But EMT is a technical skill set, no different from fire suppresion, extrication, various technical rescue specialties etc. When you have to start deciding on treatments based not only on signs and symptoms, but a host of disciplines like anatomy, physiology, pathology, pharmacology, etc, you lose the comfort of simple protocol and the ability is truly measured. If you are learning those disciplines at the depth to make independant decisions, you certainly don't have time for anything else.
As an example suitable for EMS, if you have a patient in septic shock, you might have to chose which therapy, the order, as well as the possibility of withholding treatment based on presentation or comorbidity. Take my word, that is an art, and it cannot performed well by people who are responsible for 10 other things.
I stand by my statement, any department where the individual providers are expected to perform multiple skill sets rather than a dedicated role, they are simply a jack of all trades and master of none.
When any of those departments can fight fire like a dedicated engine company, ventilate and search like a ladder company, etc in a cities like NYC Chicago, Cleveland, LA, or Miami, then there is something to talk about. Until then, it is simply "acceptable" or "the best you can."