But Shao's case already showed that such a thing was impossible. The Bai were perfectly willing to cut off their nose to get closer to Voldemort spite their face.
Shao 'helped' the Bai by killing all the morons first before doing a general cull and shake up after all the factionalisim lines were drawn. That way Meizhen's aunt had a generally easier time pushing her changes through the Bai's throat.
Killing the people at the top generally doesn't work, especially for cultures. It just makes people *angrier*. Hence the increased hate and xenophobia against non-Bai. Like, the Bai reactionary and isolationist factions still exist for a reason.
Suzhen is really only succeeding because of her strength. Otherwise she would have gotten assassinated like her sister. Even then, she has more than 1 rival for the throne, and her main one is fully pushing the isolationist agenda.
She's pushing for White because the Bai respect strength above all else, so people would HAVE to listen to her.
And also, Shao killed reformers too. Fuxi was a reformer at the end of the day, but he was dealing with the Bai at their Worst™.
There's no little killing being planned only extermination. War is an extension of domestic policy and every strength of Suzhen's rule is intended to be used against the Sun by the Bai. If the Sun had been able to secure a legacy of White cultivators Shao could look beyond murder in this generation but right now he's staring genocide across the river and only him to keep it out.
I mean, the Bai don't go into the Jungle. The one time they did, 9 Sovereigns got killed. So, I highly doubt they venture into the jungle to kill his soldiers, unless they come towards them first.
Poisoning the jungle is totally on the table though, but they've been doing that for millenia. Even at the sect, Sun Liling was the one who started fighting with Meizhen, not the other way around.
As long as they have the Jungle, the Sun really can't do anything to the Sun. Apart from assassinations. But they assassinate everyone (like Emperor An's wife). And nobles generally assassinate each other too (like Renxiang and Han Jian).
Sun Shao wants to kill them because his literal worldview is Us vs Them, and everyone apart from his abstract definition of Family is Other. Like, he's considering going against the Empire too since Xiang isn't fueling his war like An did. That's more likely to end his family's life.
The reason Shao doesn't have a successor right now is because he's sacrificed all of them to fuel his wars. So he had to make a deal with a spirit everyone in the Empire hates and nearly break his great granddaughter.
TLDR:
Generation trauma that supports toxic culture doesn't get rid of said toxic culture, even if it gets rid of higher ups. Suzhen's mostly succeeding because of her strength. That's why she's pushing for White.
The Bai really aren't in any shape or form ready to exterminate the Sun and can't because of the Jungle. Instead of actually building a strong line of succession, Shao sacrificed his family to fuel his wars.