Preserving Privacy
Long before Archie was born, there were rumors that he was darker-skinned than the rest of the family. It was reportedly one of the first topics brought up, which was only a few months after the pair married. Meghan was presumably aware that her future kids would be treated unfairly in comparison to their cousins.
She may have been concerned that Archie, too, would be subjected to such harsh attention from the general public. Even though many people supported him, some would have seen him in a negative light because of his skin color. That could be why the couple decided to keep Archie out of the spotlight.