Or they could be logging in 4 times a turn sending loads of private messages back and forth to their co-conspirators, planning a rebellion. They are, after all, hoarding gold in the capital while everyone else goes off to war.
Indeed they could. If they were doing that, though, they would be much better off actually following orders.
If that was the suspicion, then it would be easy to prove. There would be a letter from the king to the judge saying "Ban those people because I suspect they are organising a rebellion."
But that's not what was said. They were banned for failing to answer letters.
I don't oppose banning in general. I don't even oppose banning for spurious reasons. I oppose witch-hunts to get rid of inactive characters.