Healthcare: Third-Party Billing

Hey Nationites,
I severely apologize for this boring topic. I have a debate I need to prep for in one of my Athletic Training courses. I have been assigned the side of speaking against third-party billing for Certified Athletic Trainers.

Are there any economists, accountants, health-professionals who could help me out?

Why wouldn’t we want third-party billing as an allied health professional?

WOULD this be like having my insurance pay to have CT train me?

I can see that it would be yet another health care cost, and even though it would be preventative, it is still a cost.