I like this theory a lot, but I genuinely think Aokiji could just have a common goal to Blackbeard of destroying the WG. Seeing the depravity of the Celestial Dragons personally as an admiral and committing atrocities like Ohara for the WG all while trying to work for the goal of reforming it for the greater good only to fail and have a psychopath like Akainu take over was probably a huge gut punch for Aokiji sense of Justice. He knows about CP agencies and the horrors they commit. I think with what he’s seen and done for the WG that he could come to a conclusion that the WG must be destroyed and BB is the only man strong enough to do it that will do it (ie Shanks may not think toppling the government is worth the collateral damage) and his arc will be coming to trust that Luffy will do it. For as bad as BB is he’s more or less pragmatic and reasonable for a villain. I could genuinely see a gentleman’s agreement to destroy the WG. It’s still probably a SWORD thing but I could see it being a genuine alliance of circumstances.