Those prices don't include a bunch of things you'll also need, which makes them a little misleading. Some of those things are predictable, and some, like your housing costs for the duration of your recovery, are not. In a typical hospital setting you're paying to stay in a hospital bed, and they can't tell you how much that'll cost ahead of time.

It's probably a lot easier to determine all of these costs on average rather than per-patient. Medical staff could be paid a salary, and hospitals/etc could set a budget based on average costs and workloads. Then a single-payer system could collect the money needed into one big pool and pay it out based on those budgets.