thats ultimately why he diverged from the previous group and he will from this one too.
I don’t think he’ll diverge from the BB Pirates, he left the Marines because of Sakazuki who was being backed by the world government specifically and likely because he didn’t want to follow sakazukis orders.
Blackbeard pirates seem free and are given a good amount of autonomy. The only thing Kuzan seems to have been ordered to do is take down an emperor crew, something he wouldn’t have been able to do as a marine admiral due to the red tape.
So he honestly has been given more opportunities to fight for Justice as a BB Pirate than he ever did as a marine.