I don't really see his main purpose in going over there to get defeated in some sort of grudge match.
We know two things that set Perospero apart from the other BMP:
1) He actively opposes the BMP-Beast Pirates alliance, even calling Big Mom insane. Others like Smoothie choose to obey Big Mom, others like Daifuku are not worried about the alliance and want to focus on capturing Luffy first.
2) He specifically hates one of their members,
King. No other BMP has been shown to have resentment toward any particular Beast Pirate.
We also know that Perospero thinks highly enough of himself that he believes he could lead the BMP in Big Mom's absence. In other words, he believes his judgement is above the rest of his brothers and sisters. Perospero believes his thoughts and actions are representative on behalf of the BMP.
This sets up Peros to be a some of sort of homewrecker. Oda is most likely using Perospero to ultimately break up the Big Mom and Kaido alliance. Perospero could attack his allies like King, he could make his opinion known that the BMP are never trusting the Beast Pirates, he could invite some sort of third party chaos that destroys any sense of union or cohesion leading to their dissolution.