If my wife started bleeding profusely and seconds counted, I want her near a hospital surrounded by trained medical personnel and doctors, not a midwife. The popular belief is that hospitals too often push for C-section, but that has never been our experience with our two children that were born in hospitals in the last two years. They did everything they could to avoid a c-section (we were close with the first one, as they had a little trouble getting him out), and both our children were born naturally.
Our two babies were born in a hospital for the same reasons as yours. And my knees were weak and I couldn’t speak intelligibly for hours — just from watching my wife give birth in the birthing suite. What times those were!
My point is: things can go wrong with giving birth, even in a hospital.