The BBP are like the Rocks pirates. The commanders aren’t strictly followers of the captain, more so a loose alliance with of characters who’s goals align held together by a powerful captain.
Like Kuzan still sees himself as a follower of Justice, despite working alongside pirates.
Anyways Teach needs Kid. He wants to literally overthrow the WG. You need conquerors to do that and apart from maybe Kuzan, none of teach’s crew have CoC.