I think that part of it just boils down to being a professional.
The reality is that EMS and Fire (as well as law enforcement for that matter) have far more in common than many would like to admit. They both require a dedication to the science of the material, but also the art of applying the material in constantly changing environments. They both require the ability to stay calm under pressure. They both require the ability to make the best out of a poor situation. They both involve hard work often for long hours.
In both cases you will find people who do the minimum and then play on their phones, play video games, or whatever else. Regardless of whether this exists in fire, EMS, or a combination department (as well as volunteer or career) it is not a professional behavior.
My bias is that I was a former fire/medic that saw a pretty even split between fire and EMS. I think that on both sides we provided good service to the community. When we showed up with an ambulance or a fire apparatus we were trusted to be able to perform our job well both by the general public and other departments. Ironically if I showed up in one if the ambulances to a fire department they treated us like they would their contracted third service (not well), and if we showed up in a type 3 to a EMS agency we were treated as the dumb firefighters.
I can think of plenty of people that were great at both roles; be it in EMS and volunteered in fire, had a dual role job, or were in fire and had a EMS side job. I'd like the idea where we continue to advance the training and education for both EMS and fire, and perhaps both will not be doable in the future, but currently in the US I think it is very possible to be both. I also think there are plenty of sub par EMS providers and firefighters, but typically this is because they are not professionals, not because they are dual role.