A pre-nup can't really address the best interests of children. They are not property to be negotiated.
In addition, by pre-negotiating the financial considerations, the two parties might better be able to negotiate what's truly in the best interests of the children instead of weaponizing them.
It makes no sense to permit parents to agree in advance as to who should have parental responsibility. Things change, particularly when divorce occurs, and the best interests of the child is what matters - not what's agreed to beforehand.
Contracts inherently deal only with property interests of the contracting parties; they can (within certain bounds) address custody because our legal system treats that as a property interest that is subject to some domain-specific limitations and oversight, because the general premise is that it is not a natural property right, but a legal contrivance for the interests of the child because parents will normally be the best motivated to serve those interests. (Though there is definitely a not-uncommom view that children are naturally property, as well.)
Best interest of the children are to minimize parental conflict. No matter the outcome, a legal process inflames conflict.
Arab countries have this right. There is a strong presumption that kids go with mother up to some age, and father beyond. The rules are clear and simple, barring exceptional circumstances. Some of the Scandinavian countries do to. Barring exceptional circumstances, there is a presumption of 50/50 custody and child support is capped.
There is nothing to fight over, and fighting dies down. The US high stakes system, where child support is astronomical and where everything is up for fighting over, is the biggest loser here.