I agree with the others about the copays. My 30 year old son is on my insurance. I have nothing at all to do with his copays or other costs. He is on his own there. I never realized I had any obligation at all to pay for anything to do with all of that. Do you?
This is an interesting quandary because it brings up two questions.
What is best for us? To have the security to know he is insured or to be free of any entanglement?
And the other question, do we really help them and protect them by helping them to avoid the inevitable costs of their own lives?
It sounds like in this case you can have it both ways: keeping him on the insurance and not accepting responsibility for costs. He is a legal, emancipated adult. For some reason you keep accepting responsibility for these medical costs, when you are not obligated to do so. What is the payoff to you of doing so? Nobody is forcing this on you. If son could continue on your insurance with all of its benefits, without your stepping forward to take on this responsibility of copays, if there is no compelling reason to do so, why do it?