It might just be a case of Leliana proposing sneaky solutions while Cullen and Cassandra tend to favour more direct options.
I think is this. Maybe the same will happen with Scribbles, but since she's the diplomacy and trade advisor, probably the arguments will be less heated.
Everyone has his or her past, so it would be a disservice to remind them of it every time. Let's see:
-Leliana: Former bard. That means spy and assassin. For fun, at the beginning.
-Cullen: Templar. Aren't they rebels?
-Cassandra: Seeker. Aren't they rebels too?
-Vivienne: Circle mage. Yes, rebels.
-Dorian: Tevinter Magister. That should say everything.
-Cole: Spirit. If that wasn't enough, a murderer.
-Iron Bull: Qunari agent. Fomer member of the state police.
-Sera: Member of a criminal gang.
That's why the Inquisition motto sounds so appealing.