Exactly. What the US lacks is actually more liberal market in health. Less regulations and more competition.
When talking about regulations people usually mean regulating pricing and/or service quality but what actually needs to be tackled are the factors that limit competition, like: - process for opening new clinics/hospitals should have little to none restrictions - requirements for doctors (no doctors from outside can work in the US unless they complete $400k degree) - Drugs from outside countries should be allowed to be imported without FDA's approval
and so on