Let me try again...
Historically, women were not able (due to cultural bias and discrimination) to earn salaries that allowed them to take care of themselves and their children. Marriage was a form of income security. Alimony (adult support) along with child support was often a necessary legal measure to maintain income security. Society always views men as being able to secure income; this is why few men receive alimony in divorce settlements. Today, women have acheived relative parity in income earning potential. As such, the need to insure economic stability via alimony is not mandatory in many divorces. In this particular case, both parties earn substantial amounts of money, which will allow each to live well without assistance from the other party. Alimony in this case would only be punitive IMO.
The newborn child is their first, there has been no opportunity ex vitro for the child to witness any alleged abuse/infidelity (again, I don't follow celeb gossip, so I don't know whether the allegations are true).
I believe family courts should assign a trustee, or at minimum an auditor, to review the use of child support funds by the custodial parent (note my gender-free descriptor - stop trying to paint this as woman bashing) to insure that the best interest of the child(ren) is maintained first.
Again, family court is about taking care (financially) of the kids. The divorce is about ending an unhappy/unhealthy marriage.