I see people saying the reason why Law and Kid are going above and beyond to stop Big Mom is to protect Luffy and give him a chance against Kaido. Like out of friendship or respect for Luffy. I don’t think that’s entirely correct.
The main reason why Kid and Law are pushing themselves way beyond their limits here is because they know if they let Big Mom go the raid fails. Simple as. If she is let loose again she can single handedly win for the Beast Pirates.
All of the alliances strongest fighters are basically down for the count. The only one really left is Luffy who has his hands full with Kaido. If Big Mom makes it to the roof Luffy dies. And if Luffy dies Big Mom and Kaido can sweep the rest of the alliance with ease, kill every opponent. Including Law and Kid’s crews. Everyone’s dead. They lose. Same goes for if Luffy lets Kaido go.
Kid and Law know the survival of every good guy on the island rests on Luffy beating Kaido and them beating Big Mom.
They know Luffy is holding up his end and is giving Kaido an even fight, so it’s literally all up to them. They have to deal with Big Mom, their lives, their crews lives, the samurai lives, and the lives of everyone on Wano rest on them holding off Big Mom. That’s why they’re going so far into overdrive despite being at deaths door, not to protect Luffy out of friendship or whatever, but the fact that if they let her leave the war is lost.