but I would call it Medicare Part E (everyone) and allow any citizen to buy into the system (parents could enroll their children if they wish). Other federal programs like Medicare A-D would survive, along with Medicaid, VA and SCHIP.

Medicare Part E would be cheaper, more efficient and more generous than for-profit insurance. But by all means, if people want to stay in their lovely private insurance program, be my guest. Healthy people might stick with private insurance for a a little while longer, but even they would get a better deal on Medicare-E. Indeed, the whole private insurance industry would collapse in a few years anyway as more and more people leave in droves for Medicare-E.

And that would be the whole objective right there.