You gathered some good arguments, gotta give you that!
Sadly there are some tiny flaws in your argumentation.
Zuko's swordsmanship is only relevant in 3 occasions
Santoryu
Ashura
And you are forgetting that Zoro normally uses 3 swords. When he only has 2 swords, like Zuko he is
nerfed and it doesn't feel right to him.
And did you remember that Zoro can even fight with no sword style as a
brawler?
By teaching Aang firebending and then getting out of the way so the Avatar can fulfill his destiny. Not by "taking down the fire lord himself". In that sense, everyone in Aang's gang joined forces to take down the Fire Lord. Are all of them "Zoro-like" as well?
Luffy and Zoro are often portrayed as a duo , Luffy the sun and Zoro the moon.
Aang and Zuko turned out to become best friends.
And may I remind you who was on the rooftop and who wasn't? Zuko confronted Ozai during day of black sun and eos Aang fought Ozai alone while Zuko dealt with Azula who can create
BLUE FIRE.
Zoro briefly fought Kaido, then moved on to King who has
BLUE FLAMES while Luffy is currently fighting Kaido 1 vs 1.
Zuko went against his sister and lost because Azula cheated and tried to light up Katara's ass. Remember when Sanji fights Judge and Judge cheats using a human wall to stop Sanji's attack?
But that's the oposite.
Sanji has a nice sister. Zuko doesn't.
After overhearing the conversation of Ozai and Azulon, Azula suggests to Zuko that if he wants to escape death "maybe he finds a nice family in the Earth Kingdom who wants to raise him".
The Earth Kingdom was known for its Fire Nation colonies. And what else is a colony? Right, Shimotsuki village in the East Blue!
While Zuko helped Iroh fill the void left by the loss of his own son in the war, Sanji was special to Zeff due to both of them sharing the same dream, a dream that even Zeff's crew would not take seriously.
Iroh's and Zeff's motivations have nothing in common.
Really, Koshiro is Zoro's Iroh and Kuina is Lu Ten.
Did you see Zoro's parents anywhere?!
Zuko had to leave his home and so did Zoro(or his ancestors), Koshiro became his mentor and treated him like his own child. He even wanted him to become the heir to his dojo. After Kuina's death he even gave Zoro her sword.
He visits her grave to place a newspaper with an article about Zoro by her grave. While Iroh held a memorial for his deceased son in Ba Sing Se placing an picture of his son in the place where he died.
The fanart you posted does a good job at highlighting the blatant differences between Zuko and Sanji, showing Sanji as the professional that he is while Zuko is portrayed as a lost cause in the kitchen.
When exactly on his travels across the Earth Kingdom did Zuko ever prepare his own food?!
Even while travelling with Iroh, he has to steal food or has food donated to him.
During his solo travel in an Earth Kingdom town that was terrorized by
corrupted and violent local authorities that abuse their power and are feared by the citizenss he is
starving, challenges the corrupted authorities while
fending for a small child and in turn
gets food.