In Fishman island arc we found out that Kid destroyed two of the big Mom's ship, in Wano we found out that Kid injured one of her commanders (probably Smoothie) and stole samthing from her. I said it before and I say it again, Kid's role in Wano is to take down Big Mom. I touched power scaling aspects before so I'm not going to get there again.
Kid have not the same blood bond to Big mom as Luffy have, the didn´t run after Kid, the run after Luffy!!
Two commanders get defeated by Luffy, her army get weakenend, her castle get destroyed, her name get put in bad way by Morgans, the lose Zeus and many many other aspects, her blood bond to Luffy is more then to Kid.
Kid also doesn´t make anysense to let him defeat Big mom. Overall he said the same as Luffy, he wanna defeat Kaido who beat him and make Killer a pleasure, he has more blood bond to Kaido rather to Big mom as he himself state it.
Also to Katakuri, Luffy said that he gonna the one who defeat Big mom, that hold much more bond then anything, Kid doesn´t have the same bad blood to Big mom. And at this point only Luffy can be the one who beat Big mom because of all what happen in the past, no one else has the same weight in bad blood as Luffy and Big mom have.
I post many points in my previous post who don´t held much on powerscaling aspect, everything speaks against a 1on1 fight, but as I said I gonna bet with everyone who believe that Luffy defeat Kaido in 1on1 fight without any help.