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.
My daughter gave birth in December to her second child. It was a moderately high risk situation.
A year or so ago a new branch of the area’s main hospital opened much closer to us and started offering labor and delivery.
When my daughter asked if she could go to the new location, her doctor said “No, it isn’t a real hospital yet.”
Of course things can go wrong.
But when home births go wrong, you go to the hospital. When you deliver in a hospital, you're already there.
Other than cost, I don't see the benefit of home births. I would never expose my child or my wife to those risks, even if the risk was remote.