CoA and CoO are base tools, adv CoC is something else.
Adv CoC acts as a buffer between you and your opponent, it is antithetical to pure swordsmanship.
Kick's kings aren't minor, Rayleighs kicks saved Zoro's life. Sai and Judge use a spear and kicks, I wouldn't call them pure spearman. Kicks are all Sanji uses and he is on par with Zoro, so they aren't to be discounted just because you are a zorotard.
I don't see Mihawk incoporating brawling into his sword style and don't think he has adv CoC tbh.
I think Shanks and Mihawk had swordsmanship duels but Shanks' actual combat incorporated kicks, then he learnt adv CoC while becoming a Yonko, after he stopped dueling Mihawk. You cannot debunk this, we will have to wait and see, but that is the argument distilled as to why Shanks is not just as swordsman.
Adv CoC acts as a buffer between you and your opponent, it is antithetical to pure swordsmanship.
Kick's kings aren't minor, Rayleighs kicks saved Zoro's life. Sai and Judge use a spear and kicks, I wouldn't call them pure spearman. Kicks are all Sanji uses and he is on par with Zoro, so they aren't to be discounted just because you are a zorotard.
I don't see Mihawk incoporating brawling into his sword style and don't think he has adv CoC tbh.
I think Shanks and Mihawk had swordsmanship duels but Shanks' actual combat incorporated kicks, then he learnt adv CoC while becoming a Yonko, after he stopped dueling Mihawk. You cannot debunk this, we will have to wait and see, but that is the argument distilled as to why Shanks is not just as swordsman.
You can enhance your swordsmanship and sword attacks with it, so it's a part of your swordsmanship. As simple as it gets.
There's nothing as "kick user". You're either a brawler, or you're a swordsman. A brawler can incorporate sharp attacks into their arsenal (Lucci) while a swordsman can incorporate kicks and punches into their arsenal (Zoro) ocassionally. But all in all, your main fighting style and stuff decides what you are. Shanks has 312984782397498238947239873298749823 portrayals and statement that inches him towards being a swordsman, and zero towards non-swordsman.