You really don't understand the system.
1) In the US almost every hospital has to eat millions in services to the poor. Those costs are tacked onto your bill. In the state run systems the state pays for those. If that happened here you bill would shrink a fair bit.
2) In state run systems suing is not as big a thing as it is here and as a result liability insurance for health providers is much less. That adds a TON of costs here.
3) In state run systems there is less perceived need to practice defensively. That lowers costs at the price of increased medical errors.
4) Medical education costs in the US are borne by the practitioners and it aint cheap. That raises costs to the patient.
TL: DR These are very different systems.