No, he wants copies of the contracts.
Rachael even states things herself... SHE knows the women from before, and they're not approaching her as a fixer they heard about, they had prior friendships. As the MC, we'd be relying on Rachael to stay honest about things, rather than "well my friend isn't rich anymore, and all it would take to help her get rich again, is tearing up this contract that he doesn't have a copy of, and it's an easy lawsuit."
Except the only thing he would be legally entitled to is a copy of a contract between him and Rach saying he is a sperm donor which he didn't sign.
He has no legal right to contracts between the girls and Rach.
She certainly wouldn't give him any.
And uhh.... that's my specific point boy. The player did nothing more than verbally agree to being a sperm donor, which means this could go HORRIBLY wrong for us later because we didn't sign anything. Even asking for a written agreement as a sperm donor, let alone the full contracts between Rachael and whoever he agrees to knock up which specifically states these women are giving up any action on the players part, and that simply revealing who you were is a breach of contract.
You clearly don't understand how badly this could go, if it weren't "just a game" when you're relying on someone who had prior relationships acting as a pimp (she's literally sending you girls specifically for you to fuck and breed) and all of them are prior friends of hers, she even states that friendship outright. And we're supposed to simply 'trust' that should something happen, Rachael won't casually tear up the contract and pretend one never existed.... why exactly?
Edit: Also, multi-party contracts are a thing, and the "contract" would actually be between the woman and the player, not with Rachael. Rachael is nothing more than a fixer... a MIDDLE MAN, she has exactly zero place in any contract. She arranges the introductions, after that she has no part in what happens. So you are wrong in that any contracts are between these bored, wealthy women who want to get pregnant and Rachael, all the contracts would be between them and the Player.
The best you can argue, is that Rachael would also be in the contract specifically as the fixer, as she is taking 80% of the profit for being the one arranging everything. This means the primary signatory is the woman trying to get knocked up, signing away her right to reveal who the donor is and releasing them from financial support... Rachael is signing as she's taking the money for handling the travel and accomodation arrangements, and the PLAYER is required to sign in basically reverse stating HE can't reveal who he's banging and acknowledging that your parental financial support requirement is being waived as the donor.