Ah, but your chances of an MRSA infection aren't the same everywhere. Some hospitals are far better than others at preventing infection, while others are far worse. In a bill per procedure world, like in US medical billing, while I'd not expect anyone to do it badly on purpose, lax procedures that lead to more care are paid by the patient's insurance. In a government owned hospital, or if billing is done up front, it's the hospital's problem. American billing leads to no incentive to saving money, so guess what? US hospitals charge a lot more per procedure and perform somewhat more procedures than everyone else, so ultimately the price is higher.

Even if nobody had insurance and shopped around, the US style of billing would lead to very little downward pressure on prices, as it's impossible to have a clue of what you are going to pay.

Many businesses, including freelance developers, will not charge per hour, but by job. You jack up the price to end up ahead in the case of typical complications, but there are cases where you lose money, and that's on you being bad at estimates and billing. Billing by procedure in the medical system is just setting the wrong incentives, and a recipe for maximum waste, if not downright fraud.