I would hope it’s common knowledge nowadays, at least amongst the educated, that you should call your insurance or check their website for in network providers. I can call mine and find out how much certain procedures or codes cost, and if it’s not an exact amount, they can usually give a pretty good estimate.
Also, I would expect any service to cost 50% more in the Bay Area.
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.
Hospital stays are a whole different thing from more routine procedures. A lot of the costs are directly billed by the doctor and bypass the hospital, and hospitals don’t know what their own costs will be.
If you have insurance that covers this, it’s simple. You don’t even need to call anyone. You’ll pay your deductible.
If you want to compete on price, you’ll either need to charge substantially less than people’s dedictibles in order to make a noticeable difference, aim your price competition at insurance companies (who pay vastly lower prices already), or target the not-exactly-lucrative uninsured population.
Also, I would expect any service to cost 50% more in the Bay Area.