Which is to say, I completely agree with the overall assessment of Zuko. He isn't the type to hide his feelings and have ulterior motives.
But that only applies if he knows his feelings. I do think his refusal to move in "The Ember Island Players" was due to feelings for Katara, but not conscious ones (after all, look how they both react when the idea is brought up on the stage!).
In The Southern Raiders, Zuko tells Sokka, "Your sister. She hates me! And I don't know why, but I do care what she thinks of me." The punctuation of the transcript matches my perception when watching the episode: What he is confused about is not why she hates him, but why he cares what she thinks of him. He doesn't know himself well enough to name his reasons.
I think he enjoyed siding with Katara against the others when taking vengeance against the Southern Raiders, but again this was subconscious (and not his only motivation). He was completely sincere when admitting to Aang that Aang was right about what Katara needed, that Zuko was wrong. Nonetheless, I think there was more going on with Zuko than he himself was aware of.*
It's like in Bitter Work, when Zuko denies feeing ashamed - a denial that made me boggle the first time I watched the episode. "Driven by shame" is about how I would describe Zuko at that point in his life. He's not lying. He believes what he says. But he's not telling the truth because he does not know himself as well as he thinks he does.
Anyway, this same Tumblr person made another post that I have more agreement with: https://paragonrobits.tumblr.com/post/645970719555059712/so-the-more-i-think-about-how-zutara-would-work
I somewhat ship Katara/Zuko, but in the long run it could only work in a world where Zuko did not become the Fire Lord. No way would Katara be willing to take on the role of Fire Lord's wife for the rest of her life. I'm sure the pressure from Aang to produce an air bending child caused tension in their marriage, but if she married Zuko total strangers would be pressuring her to be the proper representative of a nation she grew up hating. I know our world is very different from A:TLA, but I can't help but think of the experiences of real-world women like Princess Diana and Meghan Markle. No way would Katara willingly go through that for the nation that was responsible for her mother's death.
*To clarify: In The Southern Raiders, I think Zuko cares about Katara and wants what is best for her. But he wants what is best for her to be revenge, because that is something only he can give her.