The harem emphasized that a son's status depended on his mother. Concubine Hui came from a lowly background and did not have a prominent family background or outstanding talent. She also did not have any connections in the court. Her son should not be a threat to the other concubines with outstanding family backgrounds in the palace.
However, what if the previous emperor valued his son extremely much? He even ignored the fact that he had a disgraceful and sickly mother, wanting to nurture him as the heir.
There were no children in the Central Palace. As long as there were concubines in the harem, everyone could fight for that position.
So what if the previous emperor wanted to pursue the matter?
That also depended on whether the court officials were willing to let the emperor cause trouble for an insignificant but favored concubine.