There are absolutely roleplaying reasons why someone not emotionally invested in it would still want to know the truth or punish a mass murderer, even if that meant trekking for 8 hours. You mentioned one of them. You don't really get to determine for others what their characters are like. How would you know? So what if you have no personal gain in it? What's your point exactly? That Watchers who have the ability to know every sin in anyone's life have no authority to "dispense justice?" I'd say they have a little more authority to do it, based on how they have more accurate information than any jury.
But you make a good point about having no evidence suggesting that all of the other woodcutters participated in the purge. Same for the Dozens, not all of them participated in mob justice. Nor are all Doemenels assassins, though I think it's a perfectly valid reason to storm and massacre the base of the gang who sent assassins after you. But, this is why I chose to lie to the Devil.
As for Raedric, you don't have to sympathize with Kolsc to want to kill Raedric. I wanted him dead before meeting Kolsc. But I didn't kill any guards doing their jobs. You could sneak your way in and kill just Raedric and his personal guards. They had a choice to defend a mass murderer or leave. They chose to stay and fight.