If an ordinary family adopted a very young child, they would most likely hide the fact that there was no blood relation between them.
But Salomon was different. He believed that, given Milia's rate of mental development, she would sooner or later realize that she shared no blood ties with him or the Witch. He wanted Milia to face the truth and not waste her time on the emotional influence of a meaningless blood relationship—an extremely unsympathetic idea, but the responsibilities Milia bore did not allow her to dwell on such matters. The Western educational notion of "doing everything possible to satisfy oneself" simply did not exist in the education Salomon had received or the education he gave others. Responsibility to the collective would always outweigh selfish personal desires.
As the Daughter of the Devil, Milia possessed extraordinary talent, but as a pawn the Outer Dimensions used to manipulate the Material Plane, she was destined to have little personal freedom. Under Salomon and Bayonetta's protection and affection, Milia could grow up healthy and happy. She could even grab hold of the gaps in the Praetorian Guard's and Salomon's Power Armor, climbing all over them, making as much trouble as she pleased, and learning whatever knowledge she wanted. Even so, she still had to face the responsibilities and curse she bore. That was a reality she could not escape.
If this had been an American superhero comic or television show, Milia would have risen up against her adoptive father after discovering her origins, rescued her birth mother, and then made her debut fighting crime on the streets. Perhaps there would have been a later arc where she discovered her responsibility and bravely shouldered it, only to inevitably mess everything up and plunge humanity into a massive crisis, until prepared adults came