I don't see how that ability would make any sense though? Turning someone into rubber is like giving them an upgrade. Since they become resistant to physical punches... which is what Luffy uses to fight.
I think it was just the cartooney style that Oda wanted to go with.
It maybe but Kaido actually commented on it last chapter. "You're supposed to be rubber not me." If it were solely for comedic effect I don't think the character would react to it. I mean all those people who's eyes popped out didn't go like. The fuck is happening to our eyes? And now in this chapter we can actually see that Kaido's skin stretching alongside the punches.
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Why it doesn't prevent the opponent from feeling damage I dunno, perhaps the combo of haki? Or it impedes them more since it's a foreign influence? All speculation really.
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Also the resemblances between this form and the energy steroids. Hody and his crew also turned into elderly after using them and it was a secret treasure.