The thing is that the emperor's power is limited. That's why we have so many dynasties.
The great houses influence and change the direction of the empire, and they grow and wane in tandem to the empirical power.
You can't baselessly accuse the sons and daughters of the duke that holds half the military power, or the merchant that has all the neighbouring kingdoms in his pockets. It's just not reasonable and if angered enough, can lead to being labeled a despot and getting ousted or over throne. You've seen how these houses where quick to aline themselves to their interests when they followed latrasil, after all.
You need hard evidence to convict important people, and most of all you need the emperor's favour. Otherwise the judge, the lawyer, the prosecutor, the procurer etc just won't be willing to stake their lives on harem power struggles.
Im only 40 or so chapter in and, Like I get she just became The Empress...but why tf cant she hold a meeting or something to quell the misunderstanding/jealousy they all have over her being busy or something at least. Its kinda annoying to see a petty fight every chapter or so that just gets resolved by ignoring it cuz there isn't any evidence