Because otherwise she'd also be executed after their ruin since she's also a part of the family.
Back then most of the time, if the family fell EVERYONE fell. Even those who weren't involved.
Cause she don’t want to die, duh ╮(￣▽￣)╭
She would go down with them if that happens, if she aims for the heir seat. she can prevent that from happen and everyone will have to bow before her.
Why in the world does she want to save her shitty family, none of them are likeable anyway