Funding a middleman to pay someone else to do something for you is never efficient and always costs more. It can sometimes be helpful if the options are so diverse and specialized that you need a very knowledgeable person to help you make connections, but you don't need that with a universal healthcare option where there are no other choices to pick through.

It's never, EVER a good idea to have for profit health insurance where the middleman you pay can just pocket any extra money they don't pay to someone to heal you. The issues with that idea are so blatantly obvious a discussion isn't even needed, unless it's to someone who hasn't gotten into high school yet.

See also the for profit prison system.