> With respect to financial responsibility, if the cost of the delivery is a concern...

As the GP noted, if you don't even know the order of magnitude to expect, the cost will always be a concern. The upper bound on the price is in the trillions, after all.

> If we start making hospitals list prices beforehand, then they're going to have to raise the base price for an uncomplicated birth in order to subsidize those that do experience complications.

This function is currently performed by insurance companies; a frequent criticism is that insurance should limit itself to true emergency situations, but when any routine operation can balloon in price unexpectedly, it's not irrational to want its purchase mediated through the insurance provider.