You seem to pass over the third option -- a good, old-fashioned midwife.
The office of midwife is about as old as mankind itself. There was not a time when women delivered babies by themselves. There WAS a time when most women gave birth at home, with women assisting them (midwives).
I agree -- hospitals are not the best place to give birth, for a whole host of reasons. Too much intervention, attitude toward the human body and the birth process, atheistic philosophy, lack of traditional knowledge/common sense regarding childbirth, etc.
But midwives are NOT a bad or newfangled idea! It's simply a woman -- trained in the art -- who assists you with giving birth. She knows all the quick remedies to most of what can go wrong -- and she knows when to send for a doctor.
You haven't been on this forum long, but you might read some of my older posts -- I'm all about living like it's 1890. I live on 5 acres, I have an orchard, a garden, I recently got some chickens, I don't have any "gadgets", not even a cell phone. My house doesn't have a TV. So I'm all about going against the grain, especially where it helps my soul, my body, or my family.
But giving birth alone is something for emergencies only. It would be imprudent to choose it on purpose, if you could afford a midwife.
I notice you mentioned midwives in passing, but wrote them off as being about "empowerment". That's just how they reach the modern woman, to appeal to the affluent/middle class woman who likes the idea of having a "natural" birth -- let's face it, modern-day midwives have to make a living.
My wife made use of a midwife for our 3rd child -- our first normal birth! (The other 2 were c-sections). She didn't preach anything about empowerment to us.
Remember, God created food for us, too, but we can only eat through hard work -- that was the punishment after the Fall. Had Adam & Eve not sinned, delicious, perfect and nutritious food would grow as easily as weeds do today, and women would have painless and effortless childbirth. But since the banishment from Paradise, EVERYTHING has become more difficult and complicated -- controlling our lower nature, procuring food, going to heaven, acquiring knowledge...and having children.