Meh - kind of depens on the Mom. Mom tells the truth to the kid, supports the dad during his incarceration it won't matter, kid will still be proud of dad. Statistics are pretty wothless in this case because the dead guy deserved it and that will change a lotThe numbers on fathers in the house and out of the house tell the story. Fathers in the house is better than not. So statistical your statement is not true.
You can look it up and see. It's the way we were designed to be. Even when a father is gone working for long periods it's not as beneficial as having him in day to day life. I understand defend your family and in the face of real danger even giving your life is understandable.