Crewman Cutler was never referred to as a nurse, but as a "medic". I assumed a medic was like a first responder, someone with enough medical training to stabilize a patient in an emergency, but not a substitute for other medical personnel. A nurse has far more training. I don't believe we ever see Phlox do surgery or other complex procedures, but I suppose a medic could double as a technician who could help him.
It's convenient too that Phlox doesn't need much sleep. He's literally there all the time, which eliminates the need for shift changes. Still, Phlox seems a little too perfect. He's able to cure all kinds of stuff single-handedly and in a short amount of time that other entire medical teams can't cure. And this seems to happen in multiple episodes. (Dear Doctor, Augments, Observer Effect, etc)