Huh. The New World sure is a mess. Kaidou panics over Big Mom showing up, yet King alone seemed enough to take them down–even if it's through taking advantage of his mobility and their vulnerable position. I trust Big Mom will come back, but it's weird to see how reckless these top of the world pirates can be.
Kaidou seems to be afraid that Big Mom will tell people some of Kaidos shameful secrets like for example debt he owes her that was mentioned earlier. I think he was afraid of that more than fight itself.
Also I wonder if Big Mom will use Germa 66 snails to reach Wano easily.
–- Update From New Post Merge ---
Who said anything about fighting her?
It would be better to send Kizaru to kill or capture Katakuri and Cracker. That would weaken Big Mom forces big time and its safer than attacking Big Mom directly.. Then Blackbeard could try to take over Big Moms territory. Though Katakuri is too likeable for it to happen..