It’s not only about how the father feels in a situation like this. It’s also about the message that sends to the child, who has now seen (and will continue to see throughout their childhood) subtle messaging about the role and responsibilities that each parent takes on, and the perceived value of each parent in caring for them. A message that is heavily imbalanced, yet will influence their own view on things as they grow up.
Granted, I absolutely hear what you are saying. Not to search very far, I have cousins, who managed to get bamboozled their father was an absent father, because he was a trucker and clearly did not love them enough ( apart from ,naturally, securing their future several times over, but as kids they could not understand it -- and their mother certainly was keen to capitalize on it ).