You are wrong. What you just posted is how you define a swordsman. You are going against Oda.
Oda told us Shanks and Roger are swordsman.
While Oda told us King is not a swordman.
If Shanks and Roger weren't swordsmen Oda wouldnt have called them swordsmen. Especially not in an art that has Zoro and Mihawk.
King does use his sword to cut.
Here is King cutting off Marco's arm/wing with just his sword, not flames or even haki.
Here King is using his sword with only haki, no flames, to try to cut Zoro in a swordfight.
Here is Shanks using his CoC skills to channel CoC through his sword to create CoC burst without using it to cut.
Guess who else channels CoC through their sword and uses it to create CoC burst without using it to cut? No, I'm not talking about Roger. Don't know?
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The answer: Zoro
Here is Zoro using his CoC skills to channel CoC through his sword to create CoC burst without using it to cut.
I proved everything you posted wrong using facts. Your mistake is the same thing I've seen over and over again. You are trying to limit what type of power/skill/ability are used swordsmanship and how swordsmen are allowed to use that power/ability/skill with their fighting style.
You deserve this for your post:
:holdthisl: