I don’t think EMT burnout has much to do with the situations you mention, but rather whether the workers are adequately supported by their employers: given the resources to do their job, healthy shift length and scheduling, mental health care, etc. My friends who work in emergency medicine seem mostly burned out by being overworked because the hospitals are perpetually understaffed.
I don't see why it can't be both. I've also heard this from the better-compensated police. Not discussing "physical danger" or whatever mind you, but the toll of constantly facing conflict and seeing some of the worst of humanity. Not a direct parallel, but burn out extends beyond compensation. I've also heard this from social workers, who granted also deserve better compensation.
I think it's possible we should be spreading out emergency response better amongst society, but I don't have much in the way of practical suggestion.
Of course, we should also compensate our non-police emergency responders much better. My understanding is that EMTs make close to minimum wage and tend to carry higher individual liability.