My ideal replacement would be basically (I've posted this here for years):
1) Eliminating the tax deductions for any medical expenses (employers will be given strong incentives to drop health insurance, relevant citizens will have far less paperwork when filing taxes).
2) Taxing health care coverage from employers as income (employees will be given a strong incentive to ask for higher salaries instead of wasteful golden insurance plans).
3) Use the money saved from #1 and #2 to give everyone a refundable tax credit equal to high-deductible tax insurance premiums but ONLY if you buy insurance. That way you aren't forced to buy insurance, but you would be a complete idiot not to since it would be free to you. Also it means we only are helping American citizens.
4) Eliminating useless barriers that add massive costs to the system. For example, why do we need to see a doctor for simple medicines then go to a pharmacist to get it? Eliminate that useless doctor visit and cost and let the pharmacist prescribe the drug like much of the rest of the world. Doctors diagnose, pharmacists dispense. Simple, safe, limits each to their expertise, and saves $100 a pop. Same with expanding nurse practitioner powers. Same with state-to-state differences, get rid of them and let insurance companies sell anything, anywhere. I could go on and on with examples.
5) Eliminate the requirement to treat anyone. If someone was stupid enough to turn down their free health insurance, tough for them.
6) Eliminate undergraduate school from being essentially required to get into medical school. That would save a bundle for the doctors and eliminate a bunch of useless classwork. Meaning doctors can live on a lower income just fine. Plus it increases the supply of doctors by giving each ~10% more years to do their job, which lowers costs due to lack of supply.
7) Expand medical schools and internships. The biggest cost driver is the limited supply. Get rid of that arbitrary restriction on supply.
8) Require upfront pricing. How can we keep costs down when the same drug is 10x more if you cross the street to another pharmacy and don't know the prices? Sure, some things are complex and it might need to be a price per hour or a set minimum price + add ons. But, the vast majority of items like a visit to give you a refill should have a set price up front. Then you can compare doctor A to doctor B and actually reduce costs by choosing a good value.
It would still be market-based, drastically lower costs, cover just about everyone, important decisions are between the doctor and the patient, eliminate bankruptcy from being a major drain on people and the health care system, give our economy flexibility because people can work where they are best rather than whatever they can find that includes insurance, etc.