Ostracising players whom you suspect are Traitors is an objectively bad way to play as a Faithful
The whole game is about gaining as much info on your fellow players as you can. The parts we see them in the castle are just as important as the missions if not more. Its in those conversations when you're in a smaller group where you can really converse with people. Also how many times have we seen these smaller group/private conversations later being important topics of conversation at a round table. It's so easy for someone to slip up, disclose something they know that they shouldn't etc.
To ostracise Kas was just objectively dumb as well as being cruel. They gave him no chance to disprove them while also not giving themselves a chance to work backwards and gather evidence for their dumb conclusion.
We have a handful of players like this every season but Kas is a great case study for how you should and shouldn't play this game.