So suppose Medicare costs 200 bucks a month here in the US.

Why is it they pay for 80% of the bill and those with supplemental insurance that pays the other 20% costs the same as medicare itself?

At 1/5th of the bill, the cost to patients seems to me it should be around 40 bucks not 5 times higher.

So it is clear introducing a second bureaucracy means a whole other department of people to pay for the paperwork so that organization obviously will suck up at least 80% of the money we spend there just to administrate the business.
And their prices go up every year at a much greater rate than inflation would account for so it is clear it is just a money grabbing scheme at the expense of the insured.

It seems to me if medicare paid all the bills and that cost 20% more, then if we were charged 240 bucks a month we would still get the bills paid and the insured would save about 160 bucks a month.

Sound reasonable?