> Assuming we're talking about a happy family with two eager parents, what is helped by investigating the child's genetic "paternity," when the father is right there holding the baby?

Because the real father did not get to enjoy his rights as a parent? Because the child did not get to enjoy their rights with their biological parent?

Seriously, paternity fraud has three victims: The unknowing father, the biological father and the child.

Asking to keep the crime secret because the perpetrator might get uncomfortable questions is not reasonable when their are multiple victims plus the potential for medical mishaps for one of the victims.