I don’t understand. You can’t just go to the store and buy infant formula?
(I realize after writing this out that being at the mercy of your hospital sounds draconian, but it can be really really great if you have a good nurse or midwife. They teach you how to bathe and swaddle the baby, how to nurse, how to rock them to sleep, etc. All skills you’ll need once you leave)
We had to worry about my wife dying because they wouldn’t suggest a C-section and we didn’t think to ask for one (her induction didn’t take for several days). We’re quite confident they’d have let her die before suggesting one. Thankfully, we thought better in time.
The other side is nursing is hard, and so it is easy to cheat and use formula when you could with a little effort nurse the baby just fine. (Nursing is generally slightly better for the baby, but the difference is tiny. Nursing is generally a lot better for the wallet though)
It also has some similar pitfalls, as they are not necessarily specialists and it's still hard to disagree or do something else even if in your own home in the face of the supposed expert.