A NYT article about the hospital I'm not even certain does very much.
Hospitals will comply immediately :)
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.
If you make working with the govt on reimbursements too painful, many hospitals in well-off insured areas (good payer mix which is like gold to medicine) will just stop treating medicare/medicaid.