What I think would be best though, is to eliminate medicare/medicaid, hand people cash, and get out of the way.
The high-order problem with medicine isn't coverage or insurance. It's price. There are only two ways to get price under control: meaningful competition, or government price controls (e.g. single payer). Single payer would end up like public schools: one choice for everyone, probably OK quality, but not great.
I think we could do so much more here if we just created a cash market and handed people money. It's what Singapore does. It would let doctors compete on -- even discover -- what actually matters to consumers -- wait times, when procedures take place, even how comfortable the office is. I would much rather have a market with choice and variety than one that straitjackets everyone into a one-size-fits-all system that might work for some but probably won't for others.
I know people are going to worry about rare (expensive) conditions not being covered, and this is indeed a problem. I don't have an answer to this. One good thing about competition though, is that it drives innovation. Provider prices will absolutely be set based on what they know people can pay. If people can't pay as much, the only thing for them to do is drop prices.
It's funny. In a community where people are so focused on innovation, and startups, and choice, I see a lot of support for a national single-payer scheme. I would much rather take the collective energies of this community and apply them to innovation in this market, with meaningful choice and competition. Medicine needs more of a startup mindset. And for those roasting me about how it's different/dangerous/risky: what we have today is KILLING us, economically.