I corrected you there. You don't deal any damage with basic CoC. It doesn't amplify anything. Plus Advanced CoC is needed to scar Kaido.
Basic CoC is useful in strength clashes, Luffy vs Kata,Doffy,Chinjao all present.
If Kaido saw Luffy's subordinate have adv CoC, why would he dismissively proudly state seconds later, that Coc specialist Luffy and captain of said subordinate, couldn't possibly have it? Seriously answer that question alone, if you respond to anything else in this post, it is one of the worst jumps of logic around the Wano arc.
I don't understand why you even
want it to be adv CoC for Zoro, as that would be a massive L for him to have less of a shock factor using Asura than Luffy's base punches immediately after.
Luffy didn's scar Kaido, Roger didn't scar even base Oden with his adv CoC, so no.
Nothing to do with scars.