Depends on the state, but so many laws are now phrased in the best interests of the child, that I would not say no in all cases.
In war, adult males are canon fodder. In peacetime, they are economy fodder.
Even worse, the females know this, and CAN leverage it in many different ways. Get pregnant by Chad, quickly bed a “good candidate” Mark, happily announce to Mark that he is the father, and off we go. If Mark contests and by some mechanism can divorce the skank and be absolved of support, on to the entitlement gravy train she goes. Life is good!