@Kayriel
Easier said than done, I'm afraid. Given the feudal setting and what was shown in this chapter, it's very likely that those nobles have their own armies. If central authority antagonizes them too much, they'll revolt. Which is exactly what happened in the past. They killed all the Truth Officers and the king had to bow down, because the throne obviously can't control them all. No bomb collars for them.
Tilica's explanation also implies that in the past Truth Officers might have acted against "minor offenses", people who "embellish their words", "don't mean what they say" or commit "small wrongful practices here and there". Every government has skeletons in the closet, and since Truth Officers in the past were allowed to conduct political investigations without any lead or testimony, it would be too easy for many nobles, even the less corrupt ones, to think that the Truth Palace was a ploy by the king to undermine their authority.