There are arguments to be made for medicare-for-all, but that it is the absolute minimally complicated solution is observably incorrect. One counterexample suffices to dispel a claim of being the least member of a set.
For example, the healthcare system the USA had for well past the first half of the 20th century was "pay workers a middle class wage and control costs so the average family can afford housing and pay for medical care for their 5 kids. And then send them to college after." Nothing is simpler than to be told the price of the service ahead of time and then pay for it. I know this because my father lived through it. He was the child of dirt poor immigrants, only got a high school diploma thanks to being drafted out of college, and still managed to pay for medical care for a wife and six children. He told me about how insurance started as just catastrophe coverage, and then just grew and grew until the entire system became the morass of red tape, inefficiency, and rent-seeking it is today. Just like with student loans, having the monetary sovereign spend money into existence (directly or through high interest loan guarantees) will inevitably wildly inflate prices in the affected sector. To an extent it already has.
This isn't a simple static system. If it were, then sure "government pays for everything, good to go" would be correct. Unfortunately the reality is that it's a dynamic system, and providing a payment guarantee with politically determined pricing is "government pays for everything, so now every middle-man, lobbyist, special interest, rent-seeker, and every other assorted grifter is going to wet his beak". And that's just the beginning of the higher order consequences. Maybe medicare-for-all is a good choice, I just don't know. And I won't know until I see a cogent, rigorous, and complete analysis of the second order and higher effects of the policy change. I'm not aware of anyone offering that analysis.