I like that she has taken a level-headed step in dealing with THAT (like cooperating with the count to present evidence, though the duke is trash and probably going straight to execution is the most satisfying way to end his role in the story) but public condemnation (with evidence) is way more effective and it gives relief and trust once more to the people who still believe in her
@Ethereally she's from a modern era, of course she would handle it civilly and not just cut him where he stands. It's not like she hates her boss to the point she wants to kill him.