How about if you can’t post the prices, you simply aren’t allowed to bill for any services?
In general, I’d love to see the same consumer protection required from auto shops applied to a hospital. An auto shop must give an estimate in advance.
Also, I'm pretty sure you can write a contract that doesn't have an upfront price.
A contract has to have defined consideration, otherwise it is not a contract. Time and materials (hourly rate + cost/plus) is another standard form of financial consideration, but "we'll charge you whatever we feel like at some later time" is not.