Most women will fight like hell for custody. Not necessarily because they care about the kids so much, but for the checks and the additional leverage over their ex.
That's my point. Wives file for divorce in two thirds of cases, often because it is advantageous to do so. They get the income and assets of the husband without having to actually live with him.
Take that away, have divorce mean that they walk away with their personal belongings and that's it, and the divorce rate would drop sharply.