Seems a lot of people have forgotten that Law also wants to be the Pirate King.
Man SO many people have misunderstood this arc so badly. Law never wanted to war with Kaido. His plan was to pretend to want to dethrone Kaido to get the Strawhats to help him. Under the ruse of wanting to destroy Kaido's business to draw him out, they'd destroy the SMILE factory that Doffy owns. That will cause Kaido to go after Doflamingo and kill him, which was Law's real plan because of what Doflamingo did to Corazon. Law was using the Strawhats to get Doflamingo killed.
As you just said he was using the strawhats to get Doflaming Killed. It was his plan all along, he ventured to New World just for this, to have revenge for his fallen comrade Rosinante but what now? Being PK? No. Finding OP? Yes. Law has no motivation or direct goal of becoming the pirate king but if luck happens and he becomes "the pirate king" he has no objections to it too. He is carefree and goes with the flow as we see from his statement "If there is a seat open, WELL TAKE IT!" meaning he doesnt mind if someone else become PK and he wouldn't compete for it but hell take it if its granted to him. I don't see how his character would develop if he becomes PK for it is not his goal and his backstory showed it that he didn't even planned to be a pirate, circumstances made him a pirate. The only motivation he has now to go to raftel is knowledge about the D. and what would make him more likely to achieve that? Yea, being a strawhat or sailing with them. All in all Law doesn't want to be PK but he wants to find OP.
I might be wrong but doesn't Law wants to find OP?
Yes he does, for knowledge but PK? no. What would he gain from being PK? Fame? heck he doesn't even care about his bounty. Gold/Treasyre ?maybe, but hes not that type to obsess on such trivial things.
P.S. haha sorry for necroing an old thread

just got back from Finals month and felt the need to reply XD