Maybe our constitution simply rules out federally administered healthcare.

I really doubt that. It has no language anywhere saying health care must be private and it does have language about the general welfare of the people. So I think it comes down to money. If Medicare-for-all is cheaper than other alternatives, then I think it wins.

And that leads to the buy-in cost question. Obviously it is not fair to just sign everybody over 50 for free. People over 65 paid all their working lives for Medicare. That's why you need to move gradually or else charge people near as much as they pay for insurance now until they reach 65. There are a myriad of options for this, but the key is to get people over 65 to believe the new system is going to make Medicare stronger.