It is my dream that the nation's EMS system will be 100% staffed with full time personnel, who are able to handle all of their call volume on their own in a reasonable (as defined by the AHJ, the authority having jurisdiction) response time, without needing a first responder to "stop the clock." Of course, there will be calls where the FD is sent for manpower or specialized skills (MVAs with entrapment or as traffic blockers, cardiac arrests, technical rescues, etc), but they wouldn't need to function as medical providers, but just as extra hands who can do labor or provide specialized skills.
However that's not realistic, for a variety or reasons.
1) most urban EMS systems will bandaid an understaffed EMS system with a fire engine first responder to stop the clock. This is especially common with career or combination fire departments in cities, and the suburbs, but volunteer first responders are common in the rural areas too, for the same reason.
2) the AHJ determines the appropriate level of service, the appropriate level of staffing, and the appropriate funding model.
Is there a place for volunteers in EMS? Absolutely, as a 3rd person, while they get trained up to a certain level, but once they are cleared to drive and be an essential part of a crew, they should be converted to a part time employee.
That all being said, the US will never have my dream EMS system. There are too many rural areas where there isn't a large enough tax base to fund a full time EMS system; what happens is the AHJ gets tired of extended responses, and forms a volunteer BLS EMS system. the response becomes "it's better than nothing, which is what we have, and cheaper than a full time ALS system." And too many government leaders are not willing to provide adequate funding and staffing to EMS system, because many don't care about EMS until it affects them personally.
Remember, it's rarely the case where there isn't money for EMS, it's that the money is being allocated to other priorities of our elected leaders, based on the wishes of the AHJ.