I think my real problem with Biala's 'plan' is that she didn't have to go that route. She had the perfect opportunity to have her cake and eat it too if she'd let Ser Michel kill Gaspard then called in her favor. The Civil War would have ended without the risk of Gaspard, who doesn't care about the elves, winning, she still would have owned the Eluvians, and she'd have retained her power over the Empress. She'd have been in the best position she could have hoped for to effect long term change.
And let's face it, even if every human in Orlais knew the password, the Eluvians are all but closed to them if the elves don't want them in there, given the ridiculous discrepancy between elves and humans inside the network.
As it is, she risks putting her people in an even worse situation once one side or the other wins, because they aren't going to forget that the elves prolonged the conflict. She risks turning Celene from pro-elf reformer to anti-elf crusader, and she risks pushing Gaspard from apathy to hatred. Even if she wins, she's destroyed any hope of anyone ever trusting her again, and that will absolutely matter down the line when it comes time to make friends so the various human nations don't eat her people alive.
Briala already points out that Celene would have gone back on her word to help the elves the moment it compromised her position with the nobility, which is why she didn't support Celene. "But when the nobles protested, when it threatened to weaken the empire, you would have
let it go. You would have ignored your promises to me, knowing that I would always forgive. That I would always stand by your side."
As Briala says, "I will fight for the others who have no one to champion their cause."
Felassan gave his life because he thought Briala could succeed in freeing her people, so I'm not sharing the abysmal outlook on her endeavor that some of you seem to have.