I kind of think you're looking at this backwards. The Bai are a solid piece of evidence that enlightenment and superhuman intellect doesn't make you make good decisions.Yeah, the first solid piece of evidence that enlightenment and superhuman intellect doesn't help you make good decisions. It's one thing to rebuke a powerful clan once in a while. It's another thing entirely to frame one of their top up and comers to get them executed unless you intend to walk that line forever. Because the Bai have long memories, and they're not likely to forget those who tried to gutstab them while they were down.
Well, that, or having a solution to them waking Grandmother Serpent when they realize that their enemies will never allow them to rise again.
As a clan the Bai have a reputation for never forgetting a slight, seemingly coming from their snake heritage. By that measure repeatedly kicking them when they're down is a perfectly sensible move if you've ever offended them in some way, because the Bai will fuck over everyone who 'insulted' them if they get back to the top, and will devote themselves over years, decades or centuries to doing so.
Plus grandmother snake is not something you wake lightly. Given what we've seen of Cui it's perfectly possible that Grandmother snake horribly kills anyone who wakes her up for the insult of poking her hard enough to wake her. I think it was also implied that she was powerful enough that waking her causes natural disasters, possibly wiping out anyone of her own side who happens to be in the area. Finally, she isn't the only sublime ancestor in the empire, she could eventually be brought down.
So maybe you can't actually wipe out the Bai. But keeping them as far down as possible without convincing them it's bad enough to risk MAD makes a fair degree of sense once you're their enemy. Plus fear based reputation, someone, somewhere probably had their mother/father/grandfather/cousin horribly killed and is just as devoted to revenge as any Bai.
Waking Grandma Snake always struck me as the 'we're all gonna go anyway let's take them with us' and despite everything, they're still a ducal family. Still immensely powerful and feared/respected. They aren't exactly in Chu Song's situation, they have plenty more space to fall.