He's a ridiculous mary sue, which is impressive, because you aren't supposed to be able to be a mary sue when you actually are the antagonist of the story.
Like, it's not so much him as how the world reacts to him. Everyone who likes him is a good guy. Everyone who dislikes him is a bad guy. The world bends over backwards for him, no matter what he does or how nonsensical. Everybody else is a complete idiot when it comes to Tavi - Reasonable plans suddenly become things of glistening genius that nobody but he could possibly have come up with, and then every other character fawns over him for it. The roman wanking is a symptom of this, interesting enough on it's own, but because all the caricature bad guys dislike it and Tavi likes it, the plot dictates that it has to be a revolutionary idea, and all the mean ol' bullies will see how amazing Tavi really is. His romance subplot is treated in that way that all mary sue romances are treated, like it's some transcendental thing that is deeper and more profound than any other love.
Kitai is more or less an extension of that, but she's just not that great a character. She's defined almost entirely by how she is in a relationship with Tavi. She's okay, but by default you need to remove her if you remove Tavi.
Isana, oh christ, don't even get me started. Her entire character arc is one long sob story, and then suddenly she turns out to be one of the most powerful characters who has such a profound understanding of the underlying mechanics of the world that nobody else could possibly operate on the same level, and starts doing the Tavi thing where the world bends over backwards to point out how amazing she is and she starts running down the list of admirable traits like she's ticking off fucking checkboxes.
They're shit. Max was a good character. Doroga was a good character. Amara was a good character. Butcher did a lot of things in the Codex Alera right. Tavi, Kitai and Isana were unfiltered garbage, though/