American here. I dont have the answer but these are my thoughts.
a 4th wing of the government gets created, appointed by popular vote - it has oversight over everything beneath this paragraph. funded by legislative branch, veto powers over it held by the electoral branch, and life/death/malpractice issues decided by the judicial branch. the 4th branch controls nation-wide medial staffing, coverage/who is allowed to get what treatment, R&D, and building new/repairing existing medical infrastructure.
first of all I’d wipe the slate clean - immediately and permanently scrap all current healthcare and insurance systems. get rid of all private medical/drug companies. they all get broken up and assimilated by the government. no choices, it’s what gets to happen. no golden parachutes, no buyouts, no backroom deals. elimination.
the current system isnt going to provide the same level of healthcare that we have now to everyone, its just impossible - but R&D is now run by the government,… so gene therapy for diseases that only affect a few thousands of people dont get funded. perhaps they get treated internationally, or die. doesnt really matter - the goal is to treat as many people as possible with as few resources as possible, as cheaply as possible, for as long as possible. no one is allowed to stay on life preserving machines when they’re too old or ill - we pull the plug. machines are useful if you’re in surgery and only then. you can choose not to get medical aid but if your wages arent getting garnished to pay your fair share, and you get hurt, well, too bad. opting into the national health plan = opting into organ harvesting if your brainbox goes flatline and the organs can be better used by someone else. no more burial at death, it’s incineration only. religious exemptions are not permitted.
structure the system so that medical personnel are paid according to position - not by experience/seniority, or how much education is needed. flat rates. no unions, no organizations, no private practices - the system is run by the 4th branch of the government, and they set the rates. pay rates would be linked to national inflation rates. the number of specialists would be tied to population of a given area - that includes plastic/cosmetic surgeons as well as sex change specialists. traveling across the country to see a specialist is not permitted - they come to you, within a limited geographic area or you dont get the treatment you want. best cosmetic surgeon not available? go travel internationally if you dont like it, we dont care. need an emergency dental procedure? visit the hospital, a generalist will see to you - private practices are no longer permitted (it’d be filed under malpractice).
automate as much as possible - many if not most administrative positions cease to be a thing anymore - medical billing? lol we have software for that. insurance? a thing of the past, your wages will be garnished to fund the program. hospital administration will likewise be cut by 90%, automated away by software.
this would fix a lot of the issues that people in America have with the medical/insurance system - but it would introduce a lot of the issues that socialized medicine has in countries like Canada or England. might be worth a try anyway, our current system is untenable, unwieldly, and prone to error.