Yes, I know God makes it look like he discovered it, but we know that God knows everything. Jesus tended to do the same.
For example, before feeding the crowd
35 By this time it was late in the day, so his disciples came to him. “This is a remote place,” they said, “and it’s already very late. 36 Send the people away so that they can go to the surrounding countryside and villages and buy themselves something to eat.”
37 But he answered, “You give them something to eat.”
They said to him, “That would take more than half a year’s wages! Are we to go and spend that much on bread and give it to them to eat?”
He already knew they would not be able to feed them. I find it amusing. We know that Jesus knew things beforehand, like when he told peter
"Truly I tell you," Jesus answered, "this very night, before the rooster crows, you will disown me three times." Matthew 26:34 so it isn't like God doesn't know what is going to happen. I think when God does this it is for our benefit, the person realizes that God knows everything, that he knows our needs even before we do but also that we can't hide from God, we can't hide our sin. It teaches us something about ourselves and God.
She still had to answer for her own sin, so the punishment passes down but not the sin nature, that comes from Adam.
Or are you asking why should us women bare Eve's punishment? I don't know the answer to that, just that we do. I can tell you as a woman, childbirth is no joke. It's called labour for a reason. I assume it is because Eve is the 'mother of all the living'.
Genesis 3:20
Adam named his wife Eve, because she would become the mother of all the living.
So there is some form of passing down occurring. That somehow what they did before the fall is somehow inherited by us.Not just Adam and Eve were cursed, the creation is too.
Romans 8:22
We know that the whole creation has been groaning as in the pains of childbirth right up to the present time.
Notice Jesus didn't have an earthly father only a mother because if he had an earthly father he would have also had a sin nature, but he didn't. Then since he was a man he didn't share in Eves punishment, so he truly was the only sin-free man. The saviour had to be sin-free.
Plus while she sinned, she was deceived, Adam wasn't. I think that is another
important detail.
1 Timothy 2:14
And Adam was not the one deceived; it was the woman who was deceived and became a sinner.
He sinned in a different way from her. His was a more aware and purposeful sin.
To me its the difference between someone losing their temper or someone who plots to rob a shop, one is premeditated the other is not.
Also notice that creation bits and pieces are woven throughout scripture, it is not just in the book of Genesis. This is another reason why I am a creationist.