[Shujin]

I think its more of a "I want a more interesting concept", which I think the proposed idea certainly is a cool idea. Salamander Sword is most certainly not underpowered, and it can be a freaking beast in certain set ups.

However, I think I ratehr see a new weapon that plays with Burn in a similar way, though do think that this one might be too strong however.
You know, Cinder shenanigans and suddenly you have a status of over 60 burn damage per round, with no cap on top of what current Salamander Sword kinda does already? On Top of deleting Def boni? Granted there is more counter play, and even some hardcounters with this, but this certainly needs a cap atleast.

Other than that, I think that be a cool weapon.

Side note:
Not sure if you considered this Kuan, but since its burn -> The 3 rounds that you probably put in as balance tool to be able to kite it out, would basically still mean infinite as you take fire damage at the beginning of each round. So it certainly shouldn't renew/power up the effect. (I say that because I think it still powers up Clarent Call too, since its physical damage, unless that got changed and I misremember it.)