Other countries have price caps on their procedures. This makes sense to make the price for a procedure the same across hospitals. It's the same work. Marketing and Sales people should not be involved in the pricing structure of healing a broken leg.

We know that a good rule of thumb in the USA is that health care costs are roughly twice what they ought to be. So just multiply by two: We could have treated around 238k people.

Much more than twice. The per capita cost (across all Americans, not just those eligible) for Medicare and Medicaid is higher than the healthcare costs of most other developed countries before you even factor in private insurance.

What’s the rule of thumb on the pricing of military equipment?