What do folks in the US with health insurance have to pay? Insurance companies get huge discounts on the artificially inflated listed prices.
But it's really awfully complicated -- often the baby gets a separate bill too to muddle the waters. The ACA ("Obamacare") set a cap on in-network yearly out of pocket payments on family plans which, if memory serves, was around 11k in 2017. A complicated birth can hit this! Consider the costs of NICU, for example. (Oh and if an NICU nurse reads this: thank you, thank you, thank you for the life of my niece.)
As to what the insurers pays, I do not know.
The expectation is that the baby will be added to the insurance plan effective as of birth, so it's correct to bill services provided to the baby as... services provided to the baby.
And that includes dental and optical treatments. Braces and glasses are free, at least the basic type.
(I've generalized all of Europe; there may be exceptions in some countries.)
What happens if the parents can't afford it? Does he, like, get to go back in until the parents pay? If he had an ailment, and it got cured, do they give it back to him? Do they put him in suspended animation :-)?
I've never seen any paperwork in either country regarding billing or other costs, and that's as an adult.
Please note that you basically listed two exceptions (plus other Nordic companies), most of EU countries have a system that combines private insurance companies with a combination of public, semi-public and completely private health providers.
It may not look like much to those of us who hang out on HN, but if you have a normal job, serving drinks or selling stuff in a brick and mortar shop or whatever, there's a world of difference in details like who gets the bill, what you need in order to get insurance and so on.
What's actually happening is that:
1. A claim is submitted to the insurer, naming the baby as recipient of the claimed services. The parents are responsible for ensuring the baby is added to the policy within a reasonable amount of time.
2. If the insurer declines to pay some portion the hospital is entitled to collect, the hospital will send a bill to the parents, and the parents will be responsible for it, though the bill will be for services provided to the baby.
And no, braces and glasses are not free. Again, the child is billed, and the bill is sent to its health insurance company; also, the requirement is not just most basic type, it also needs to have a medical reason, so braces just because you want to look good aren't free, you need to contribute (I had to pay around 25,000 CZK for example, equivalent of one average monthly wage).
If you cannot see why that seems weird, shocking, amusing ... whatever then I don't know what else I can tell you.
Regarding: Assignment of the Tax ID according to § 139b of the tax code
Dear <name of the newborn>,
the Federal Central Tax Office has assigned you the Tax ID <number>. It is used for taxation purposes and valid your whole life. Please keep this letter even if you are currently not paying any taxes. Always mention your Tax ID when communicating with financial authorities. Please also note the information on the back.
Kind regards, your Federal Central Tax Office
What it did not pay full for was ultrasounds. Which aren't technical part of the birth. They only paid full for the first one and we needed 5, which was about $300 each out of pocket for me.
But I hear my experience is not typical. Usually out of pocket costs (even with insurance) are much higher in the US.