Many here from an EMS only background argue that sending more than two providers to a pt is superfluous, save an arrest or otherwise critical pt. I'll agree that sending multiple pieces to a stubbed toe or general feel-me-bads is overkill. EMS response by suppression crews ought to be for higher priority calls.
Having said that, consider how much longer you can last in the field with more hands onscene to help with lifting, diagnostics, scene safety, etc. I know of many a broken down medic, typically with either a career ending back injury or shoulder inj, or just general burnout and apathy.
When I'm on the engine, I'll carry the O2 and ALS bag, the other bucket FF will carry the monitor and airway bag. The driver will make sure the medic finds us, or bring immobilization equipment if necessary. Once inside, I'll interview the pt, do my assessment/diagnostics with any necessary ALS interventions, while my Lt records my findings. The FF will perform BP, pulse, hook up the monitor/12 lead (I interpret, of course) and BGL. The officer will gather info from the family as well as meds, and record vitals. When the medic arrives, we'll continue working, while the Lt gives them the story. We'll then assist with removal to the bus, I'll help with any further interventions, and ride to the hosp if needed. Onscene times are quite short typically. If the medic gets there first, we'll do as directed by the crew.
Having other hands to help greatly reduces the ambulance crew's burden, thereby reducing their stress and promoting longevity. 911 call to ED arrival is shortened noticeably as well.
Many private or hosp. based EMS agencies are profit driven, and will run the least amount of units as possible to increase their bottom line. Crews run extremely high call volume, in some cases for 24 hours or much more. Eventual burnout is inevitable. This can be dangerous both for the pt and the crew. Private EMS can also have staffing issues, making holdover of already overworked crews necessary. FD's with crosstrained personnel won't have anywhere the same degree of difficulty with EMS staffing.
I've worked in the NYC 911 system for years before I left. I'm quite capable of getting things done with only one partner and no other hands. It sucks at times, but you do it. When I first experienced fire based EMS I was overwhelmed by the amount of providers onscene. You have to know how to use your resources to be efficient. If everyone knows their role, things should move seamlessly and not be a cluster. Besides, why risk a career ending injury on a 300 lb plus heavy hitter when you can have all of the help you'll ever need? If you pride yourself with working a insanely high call volume for hours (days?) on end, and not needing any additional help with your pts, remember the old saying: "Pride comes before a fall". That "fall" can be an MVA, clinical error, injury, or taking out your frustrations on your pts.