Go all public and expand Medicare and move to a single-payer system like Canada and the UK. Or go all private by killing Medicare altogether, fixing Medicaid as a public backstop, and heavily regulating pricing and doctors' salaries and insurance premiums like Germany and Switzerland. But anything is more humane than the weird mix the US has come up with.
The government is very involved in restricting the supply side of healthcare.
The money that pushes this regulatory capture comes largely from health insurance companies, which might be the most vile industry I'm obligated to interact with on a regular basis. This is an industry that for a long period of time would refuse to cover health conditions simply because you were born with them.