I guess he can't really use "bullying" as a reason to do it, since most of the ladies/maids of the innermost and highest consorts are also noble ladies/has a good connection.
He can't fire them that easily, the most he can do is send an alert to the current emperor to make him aware since in the end, its his decision unless there was a murder like what happened to Fengming and Lihua's cousin and both were head maids of their respective concubines.
but even then, politics come to play, even in the harem, as the ladies serving the concubines are of rich families or politicians.
Its why it took so long for Lihua's cousin to get caught, one because she's sneaky and two because she's related to Lihua by blood making her status within the maids higher than most alongside her being the headmaid, none of the girls questioned her authority after all
(Sorry for the word vomit OP )
I don't understand why Jinshi is still waiting to fire all of consort Ri Shu's maids. They don't fulfill their duties and bully the consort Ri Shu. Just fire them all.