A couple thoughts. I am ignorant on they ways the Army educates its medical folks. I am also post-merge of the basic medical training schoolhouse, where all services go to Texas for their entry medical training. "Back in the day"...when a corpsman graduated basic corps school, they were generalists, with a foundational exposure to basic nursing, basic lab, basic pharm, first aid, A&P, etc. Then they could go to a C school to get advanced training, field med for service with the Marines, SAR corpsman, lab tech, RT (both rad tech and resp tech), etc. The theory was that ALL corpsman would be able to step into a sick bay, do a H&P, explain why they could not take whatever vac, etc. It is my sense that is not the way it is today.
In the Navy there is no parallel NEC for paramedic. There just isn't. Not field med (who could reasonably sit for a tacmed exam, or any other tacmed or trauma-specific cert), not SAR corpsman, not DMT. Maybe SARC, but even then the vast majority of their patient population are healthy males. Perhaps if HMs were still providing EMS on bases, but now I can't think of a base that is not subbed out to GS paramedics (making fat $ BTW). I agree that it is not a great entry-level choice, it just would not be worth the expenditure given that most corpsmen just do not operate at the full scope of practice of paramedic.
I can see it for pararescue who has a chartered role for rescue and emergency care of civilian people in not-combat environments.
I recall a similar conversation in 1993, so it is refreshing to see the military medical fields have evolved so much (said sarcastically).