Sanji isn't fighting King imo. He's not ready to beat a YC1 right now. If he is, then that'll decrease the tension in the future arcs and that too, by a lot. Even Zoro would have a very tough fight with King if they fought or fight in the future.
Kidd probably didn't want it to be a 5v1 or a 5v2, did he? A tag team of 5 will always be underwhelming in comparison to a proper hard 1v1, more so if Big Mom leaves the fight somehow and it results in a 5v1. And Luffy, as Zoro's captain will eventually get more recognition later on, even if the former does significant things. Defeating Kaido's strongest man will be an accomplishment that'll separate him a bit from the others.