They had to prohibit overlapping coverage in order to make sure that all private practice physicians accepted the medicare system, which has lower reimbursement rates than private insurance. You can pay for more coverage, because that doesn't compete with the public system, but you cannot pay for private insurance that may lead to lower access for publicly insured persons.
Yes, I did not read closely enough. You referred to new medicare for all plans, while I responded recalling similar false accusations against Obamacare. Some of these new proposals do not allow duplicate plans. Nevertheless, I don't think this particular objection makes them DOA. I believe this is an objection that could be overcome with discussion.
They had to prohibit overlapping coverage in order to make sure that all private practice physicians accepted the medicare system, which has lower reimbursement rates than private insurance. You can pay for more coverage, because that doesn't compete with the public system, but you cannot pay for private insurance that may lead to lower access for publicly insured persons.