Apart from needing more than zero CP, isn’t gaining CP the exact same as destroying your opponent’s influence?
I personally love CPs on non-Deeds, it’s one of the main reasons I was drawn to Law Dogs in the original game, and Sloane in Reloaded. I’ve only been to 1 tournament, but I haven’t seen a Desolation Row deck that doesn’t play deeds, just uses the CP from the outfit to win, I doubt it’d work, now a Law Dogs deck that starts with the Jail…