LOL! This is a good point about how Uncle Iroh from Avatar: The Last Airbender is actually just as much of an idiot as Zuko. If you pay attention it’s pretty accurate, but has just mastered the art of coming across as a wise old man. The even better thing is that Zuko is the only one who realizes this and no one would ever believe him because he’s Zuko…
I offer a different reason for Iroh doing dumb shit.
It’s not because he’s stupid. It’s the same reason a bard does anything.
Because it’s funny.
In regards to betraying Zhou, it’s because he realized Zhou was going to kill the Moon Spirit. That’s the sort of thing where you stop what you’re doing, and try to stop the insane madman from killing the Moon Spirit. It’s not something he did just for shits and giggles.