CoA haki does nullify a paramecia's body, but only their body itself. It doesn't nullify strings or mucus because they're just products of Doffy and Trebol's DFs. CoA does make paramecia's like Luffy succeptible to conventional attacks.
Buggy is a special case. Some scenes it appears that just being cut reflexively activates his fruit (haki or not), splitting himself to avoid being cut. Sort of like how some logia users avoid CoA haki attacks by creating a 'hole' in their body, as with Whitebeard's stab against Aokiji. And then some scenes like the one with Luffy using him as a human shield against Mihawk seem to imply that he simply can't be killed by cutting- but I chalk that scene up to Rule of Funny and less as hard evidence his ability works one way or the other. Buggy's power is very inconsistent even among the confusing paramecia family tree.
It doesn't nullify. If you look at what is stated concerning Haki, it's never stated to nullify anything; only Kairoseki nullifies. It's just said to be able to touch the bodies of those who possess intangible bodies which also means counter. It doesn't even nullify the intangible body of a Logia, it just makes it interact-able.
In fact, note that it never states that Haki is the power to hurt, but the power to touch. You can't hurt something that you cannot touch or interact with like a solid.
Paramecia do not have fluid bodies, they all have a body, therefore, they can be interacted with and touched. Luffy has a body, it can be touched, so what is there for Armament Haki to interact with when he can already be interacted with? He can be hurt without Haki too. He was hurt by the giant kid in Punk Hazard and it's not like they have Haki.
Anytime a character is hurt in One Piece, they always state "OOF" or "AHHH" (along with various other exclamations) after being hit which proves Luffy was indeed hurt here.
When he hit Rob Lucci's Tekkai which is basically making his body hard (a blunt attack), Luffy was hurt, we see him groan in pain and this is void of Haki.
Franky also hurt Luffy without Haki; that is not an expression of the lack of pain.
What do Franky and Lucci have in common? Franky's fist is made of steel while Lucci's body became hard as steel. All it takes is an attack that is powerful enough, and Luffy would be hurt.
In fact, that is literally all Haki does, it just makes things harder, so it's easier to hurt Luffy. Luffy isn't immune to blunt attacks, he's just got a high resistance. No Paramecia requires Haki to be hurt, only Logia since they do not have tangible bodies.
If Luffy had hit Trebol without Haki, and hit his main body, he'd have been hurt.
Is there a Paramecia in One Piece who got hit and then one came to the conclusion that the attacker must be a Haki user? Not one, you'd only see this concerning Logia.
Luffy even says IF Trebol was a Logia (not a generalisation of all DF users), my attack should have hurt him, so the ability to touch the body of a Logia is specific to Logia. Paramecias already have tangible bodies to begin with; Robin also states the exact same thing and she limits it to Logia, not to DF users in general.
Buggy is not an exception. He can be hurt without Haki.
Buggy is immune to slashes regardless of being imbued with Haki, Luffy is highly resistant to blunt attacks except they're very powerful. The idea that Buggy can be hurt by a Haki imbued swords contradicts Shanks stating that no matter how many times he's sliced, he can't be killed because they're just about to take on Shiki in the New World who'd have a crew with proficient Haki users. Would be like you're implying indirectly that Shanks doesn't know about Armament Haki which wouldn't make sense.
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