Human childbirth is an amazingly complicated process with a LOT that can, and frequently does go 'wrong'. In CA, the first-birth c-section rates range from 15% to 60%, hospital depending [0]. That's 1/6th to 3/5ths of all CA first births, let alone the obvious fact that you cannot plan a birthday. Your pregnancy can go from 'low' risk to 'life-threatening' in seconds; there is no planning for this and no hospital will tell you the bills for it.
I know all of those things can happen, but for people with health insurance, the out of pocket max will kick in at that point. But if you are healthy and want to get a lower bound on how much you'll need to pay you can request that information.
Maybe, it depends on the insurance provider; I've had ones that won't quote anything to me, not even a flu shot. Still, a lower bound is of little solace when talking about healthcare, especially your unborn child. It's the upper bound that is the issue.
How well things go during an emergency depends on how much effort you put into preparing ahead of time. Nothing new or strange about that.