I have heard that Owl but not known anyone in my lifetime who believes it & going back in time, my maternal gran and aunt who were both obstetricians + plus m.i.l., district (now community) midwife, did not believe in it; old Queen Vic (who had plenty of experience!) championed women having pain relief for childbirth & was effective! Not everyonetook all the early Bible stuff literally.
In my lifetime and for many years before women were given pain relief of various types. We know some people had a very hard time for many reasons (I do & feel if that had been my experience I would not have done it again), and even if it's easy and natural, it's still an effort, but the idea of women 'deserving' painful childbirth is positively archaic! Plus you are forgetting women who go through pregnancy and give birth quite easily and there are many of those.
You cite Christian doctrine, I've no idea what other faiths say on this subject but what about them? They were surely in the same boat.
Childbirth is a great leveller. Nature is nature when it comes to childbirth, some easy and some not, same with animals.
Btw the Adam and Eve legend does not say "Apple", it says, "Fruit", and Eve was deceived by the arch manipulator! Adam just gave in, in my opinion he was far weaker. He just gave in, "OK then". Weak man. However, only a story to illustrate fall of man, many similar stories in other traditions.