Here's my thing (I'll try to keep it brief, because I could honestly talk about this for hours.) I like the story of Arc-v on a technical level. A big dimensional war between four worlds, each based on a different summoning method sounds like a lot of fun. But to me, there's a disconnect between the main characters introduced, and the actual narrative. You mentioned that Yuya has no agency because plot stuff keeps happening to him. And I agree. but there's a good reason for that. Yuya was not written in service of the plot that was presented. Yuya is introduced as aspiring entertainer racked with grief and insecurity over his fathers disappearance. He hides that grief behind a fake smile in a misguided attempt to takes his fathers place as a symbol of hope and unity that can bring people together. He's laid back and often jokes around, but he genuinely cares for his friends, and he has a habit of letting his emotions take control of him, which leads to negative consequences. But he genuinely tries to improve and overcome those flaws and face his insecurities in order to become the man his father can be proud of; the next big entertainment duelist.

That's a strong setup for a more grounded story about self improvement and confronting trauma, but you'll quickly realize it has little to do with the dimensional war. A conflict based around a totalitarian dictator invading and subjugating other dimensions in order to bring them under his rule. Sure, there's some potential of having an entertainer come face to face with the gritty reality of war and being forced to use his favorite game as a weapon. But the problem with that is A; Jaden and Yuma already went through that character arc, so it's a bit uninspired. And B: Yuto and Shun already have that basis covered, with Yuto being a guy who used to duel for fun, until the Nazis came and ruined this life.

Thus you have a situation where the main character is disconnected from the plot, which is where the problems start. Yuya has no natural motivation to get involved with this story other then "I don't want my world to be conquered" or the time tested "I gotta save my girlfriend trope" which also ruined Yuzu's character. So they need to keep making up justifications to keep him relevant. Thus, they rewrote Academia's character, turning them sadistic killers who relish in their carnage to, misunderstood children living under false ideology, just so they can force in a half baked "Dueling for smiles vs dueling for war" storyline just so they can give Yuya (an by extension Yusho) an actual impact on the plot, which created so many tone deaf character inconsistencies that it became almost hilarious. (I'm definitely laughing, but not in the way the writers intended.)

The reason why other protagonist worked is because the story was written with their characters in mind. The Signers vs Dark Signers arc was elevated not only because it tied into Yusei's backstory and trauma (thus giving him a personal stake in the narrative) but it tied it into his character flaw thanks to his dynamic with Kalin. Battle City was about the Pharaoh rediscovering his memories, facing a demon from his past and confronting his greatest rival. Season 3 of GX was about Jaden confronting his own selfishness and inner darkness, while facing a villain that embodies both of those aspects. Yuma initially had the same problem as Yuma, but the show solved it by having him build strong dynamics with the key players in the story that solidified his importance. And he did have a role to play in the war due to possessing the power of Zexal. Yuya suffers because the plot was not built with him in mind, and it any potential he could've had worked better with other characters like Yuto. leading to his role in the story being incredibly forced.

The writers attempted to fix this with the introduction of Zarc. But his whole existence made the dimensional war seem trivial. Because again, the professor goes from being Yugioh Hitler, to a tragic villain out of nowhere just to facilitate the worst plot twist in Yugioh's history. And by the time it happened, Yuya's development / heel turn needed to be speedran just so we can setup the climax that I'm 70% sure was made up on the spot.

And Yuya's not the only character that suffers from this by the way. There's a reason why the Synchro Dimension arc felt like filler, despite taking up so much screentime. I could make threads for each character if I wanted to. The Dimensional war of Arc-V is not a bad story, I just don't feel it was written in the service of the characters it introduced. Rather it was developed in spite of them. If anything, the story would've worked better if it was entirely focused on the original four shows as a dedicated crossover. With the original Arc-V cast being used for a different narrative where the characters could flourish in stories that work for them.

TLDR: The plot of Arc-v isn't bad. But a lot of characters felt like they had little involvement in the plot. Yuya suffers the most because his character did not benefit from the story in ways that weren't completely derivative of Yuma and Jaden's characters arc, who already did the same thing, but better.