How many split families do you know where the father plays a role after divorce? How big is that role? – If your perspective is anywhere near mine, the role probably differs for each case you know. Sometimes by choice, and sometimes, depending on where the couple resided, by law. Not all countries and federal states recognize joint custody.
Researchers recently found out that this custody law not only matters for divorce but also for marriage. Men adjust their behavior depending on the law: whether they marry at all, how many kids they have, if any, and how they behave in marriage. By all appearances, the evidence looks like men gain in bargaining power if they can have joint custody. At least the men that care about kids. On the plus side that means they are more eager to marry, have kids and have them in a marriage, and have less recourse to domestic violence. The catch is that they also divorce more easily once married and keep women at home rather than encouraging them to work.
On balance, not a bad deal for both sides.