Emperors uses small groups to fight each other as Law said, ''territorial clashes'', not full scale wars;
They usually don't attack each other by bringing their full powers, as even Kaido complained didn't want BM and her crew landing, or WB and his crew didn't attack Wano as well,
While some clowns think thats because they are scared each other, the reason why they don't do that because it will create a big battle and in the end another 3rd party who is waiting can gain something from it by ambushing them right after the battle is ended, as Marines Ryokugyu tried to do, or as Shanks thought Teach was going to attack them on Wano.
Thats why BB pirates works separately without their full power until the right moment where they strike with full crew:
- Burgess went to Dressrosa alone.
- Shiryu and Laffitte went to Dressrosa to pick Burgess.
- Teach brought only 2 commanders to attack Amazon Lily.
- Attacked 3 Billion Law and his crew only with Doc Q, Burgess, Augur.
- Aokiji and Augur kidnapped Pudding from Cake Island previously.
If its another 2 commanders team like Laffitte and Devon, their mission is probably kidnap someone or something from Egghead island, if Teach goes there it will be a big battle.