Nobody can know your restaurant bill beforehand, since who knows what you will order for dessert, right? The hospital should still be able to give estimates for individual items beforehand. If they are not flying completely blind, someone must already know these numbers, it would just be a matter of making them public.

To me, the actual problem seems to be that they would like to make up the price after the fact, when they have a better idea how much they can charge and get away with. This gives them the unfair advantage of setting their own prices unchecked by market forces, and is frankly a reprehensible business practice.