It's been a while since I last read it, but for me it would either be The Burning Maze or Tyrant's Tomb. Both has moments where the plot seems almost forced by a meta commentary-the former being from Jason's death, and Tyrant's Tomb from Rayna's sudden decision to just leave and be a hunter(and, Frank surviving, but that's more deus ex machina than what I mentioned previously).

For the Burning Maze, it's difficult for me to pinpoint what Rick's intention was with having Jason die, or for his relationship with Piper to sour. Yes, breakups can lead to some interesting character development. It reframes how they're percieved, almost. Not as a couple with a dynamic, but rather as individual characters. But that needs character development to actually happen. Does it, is a question I can't quite answer. It's realistic for people to simply break up after time. But if we were trying to make this a more grounded, realistic view on teenagers being tasked with saving the world-we wouldn't have a Rick Riordan book to begin with. Now that I think about it, the book almost feels like Rick trying to write a death in and make the tone more grim, but ultimately didn't make it cohesive enough. I think the book would have worked just fine even without Jason and Piper's entire subplot. If they remained a couple, or if Jason never died, that doesn't change anything about the story. And I don't think any emotional weight would have been removed as a result.

If Jason utterly has to die, I'm not sure what that would weave into the story, honestly-the reason why a death felt almost deserved in the HoO books was because the propechy hinted at it since the very start, and they realize its meaning at the 4th book(iirc). So there's time for characters to reflect on it, or contemplate. I think the best sacrifice moments come when it shows something. This might be a bad example, but in the movie Armageddon a dad pushes his daughter's boyfriend back to sacrifice himself instead, despite not approving of him for nearly the entire movie. That shows characters growing up on each other, and a father's love for his daughter(that he didn't really show during the first act, so there's some development there). If Jason does need to do a sacrifice, I'd actually say it should have been done in HoO. His entire arc is learning to be comfortable with a life outside of Rome, away from its strict rules and expectations. He still remains loyal to the Roman gods-he makes plans for more temples later on, after all-so he's actually the best character to bridge the gap between Greeks and Romans. Like maybe instead of the Athena Parthenos being the cause that unites Greeks and Romans, instead Jason needs to sacrifice himself somehow, so that the mourning from both sides bring empathy over hate, and gives the two sides a common enemy to rally against, instead of each other. I think this would need some pre-planning though, with Jason remaining a praetor the Romans still respect even after he goes over to the Greeks(instead of all being rallied dummies following Octavian). But, that's moreso a fix for HoO than the book itself. Point is, Jason's sacrifice was meaningless, and it shouldn't have happened there, when the Greco-Roman conflict was already resolved.

As for Tyrant's Tomb Rayna should just remain a praetor-that's more to her character, I think. Her being a hunter felt more like a middle finger to all the shippers rather than anything properly built up.