If the men did so, they'd get their children. The House passed the new bill. It got to the Senate last week. The Senate, starting in the judiciary committee and then on the floor, removed the paternity registry. The registry is not revolutionary.
Most states have one.
Some senators thought the registry requiring men to act like adults smacked of big government. They thought the registry intruded into private lives. Never mind that the mess people make of their private lives is what makes adoption, and the laws to regulate it, necessary. Keep in mind these lawmakers are also grown-ups. Or posing as them.