Because he may be victim of a fraud? ie, the baby is someone elses?

Because the actual biological father may want a role in his childs life?

Because the state has a bit of interest in accuracy in its medical / birth certificate and other records?

Because many births are to single mothers and the absent father may have certain financial and other responsibilities for the child?

> The father [is] - and should be - the one who raises the child.

We’re implicitly dealing with two senses of the word “father” in this context which makes most of your sentences seem both commonsensical and ambigious.

> 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.

On paternity attestation forms in the usa there is a clause saying the marriage/legal father is not the father of record if the mother was in another relationship 9-10 months ago.

In Washington, DC years ago, there was a bill before the DC Council that basically said that any man having sex with a woman who ended up with a child was presumed to be the biological father until paternity was ruled out. So if a woman had sex with several men, all would have presumed paternity. I don't recall whether this applied only to public benefits and paternity.