Also think about how providers won't accept lower rates, so your new discount plan will only give you access to bottom of the barrel providers willing to take any patient at any price.
You are forgetting that insurance companies are a middleman eating up some of the costs, both as profits and as costs. It is a slightly unfair comparison (Medicare has more older people who have large single-issue costs, so less admin work), but Medicare costs about 2% of its costs in administrative costs. Whereas private insurance usually is more like 12%-18%.
There are a lot of details in that to sort, and no-one expects a final single-payer system to wind up quite as good as Medicare is... but there is a lot of fat to trim off the private insurance system.
And note please: we are only talking about admin fees (salaries and the like for people working there), this has nothing to do with the actual costs of care. If anything this is unfair against Medicare, since they are ruthless in negotiating their actual costs (something private insurance is not really incentivized to do at all).
