So far, we know that SWORD infiltrates Yonko crews but we don’t know the specific reason. Did Drake spend all that time undercover with Kaido just to barely help during the raid by killing a lower officer?
And, for the sake of argument, let’s assume Aokiji is with SWORD as well. So what if their goal was to find the One Piece and claim it for the Marines? I find that to be a fun idea, as it would basically add a whole new group to the final chase, and it would make sense that Oda saved their reveal for the final saga.
For that reason, infiltrating Yonko crews who have Poneglyphs (Drake and Kaido) is their best shot at achieving that goal, even if it means helping that Yonko move closer to the finish line in the process (Aokiji and Blackbeard). Big Mom’s crew couldn’t be infiltrated as they’re all family members, obviously.
You can debunk this by saying that the World Government wants to keep the One Piece a secret even from its own officials, as it’s tied to the truth of the Void Century. However, the members of SWORD we’ve seen so far (again, lumping Aokiji in there) seem to be the few independent thinkers among the Marines. They might have hidden their true goal from the World Government and are planning to use the One Piece to cause a schism or to topple the Five Elders.
Because of that, I believe that when Luffy is the one to inevitably find the One Piece, they will ally with him as their goals are now the same.
It just seems more fun than “they wanna gather intel on Yonko crews”. What do you think?