I haven't really seen anyone talk about this before so I guess I'll crawl out of my possum dresser and do it myself.
I believe Sybil is meant to be a mirror to the player.
Not the player character, aka The Scarlet Cousin / Y/N.
You. The player. The Problem Between Chair And Keyboard.
Sybil has been 'taking back' her daughters through the centuries to get the 'best' outcomes possible. Much like we learn more about what's going on in Scarlet Hollow with each playthrough... Essentially 'taking back' the character we played during the last and erasing them during our next one. We get a blank slate, free to make new choices and form new bonds. Noone remembers the previous ones. They're a part of us that we sent into the world of the game, but when we start a new playthrough, they are erased. Only we remember them. To everyone else, it's like they never existed.
Sybil talks about how she's become able to see the 'tapestry' of choice and consequence. Which threads lead to which outcomes. How she accepts the burden of what must be done, because she knows which sacrifices have to be made to achieve the future she decides is best. Just like we, the Player, have gained insight in which decision chains must be followed to get our desired outcomes through our multiple playthroughs. Without them, we can never gain the full picture of what is happening in Scarlet Hollow. Without them, we can never learn everything that is possible, in all its variations. Without them, we don't have the power to steer the story towards saving the most people possible. And even with all of the knowledge we can gather through all those playthroughs, we cannot save everyone. Just like Sybil can't. All we can do is make decisions on what is worth sacrificing and what is worth saving. Taking on that burden and responsibility is what the game is about at its core.
Sybil manipulates the people around her to steer them in the direction she needs. She wasn't always this way. But with each daughter she took back, humans became more and more like tools to her. Chess pieces. Actors in the play she is directing. Similarly, with each playthrough of the game, the player learns which responses to give or actions to perform to direct the game towards our preferred outcome. We no longer immerse ourselves in the game to behave naturally, to interact with people and the world in a genuine way. We take on a specific role to steer the path. We calculate costs and benefits. We tweak the threads. We use our power (traits) to achieve ideal outcomes, and where we can't, we cut our losses in a way we decide is best. We weigh what is acceptable to give up and what is not. Because we know what's going to happen, just like Sybil does. And as one of the achievements we can get reminds us: inaction is also a choice. The responsibility, the burden, is ours. There's no way around it.
We've all wished we could simply take all traits and give Scarlet Hollow its ideal story, its perfect happy ending. Which is exactly what Sybil wants to do by taking The Entity's power for herself. No more negative consequences, ever. No more hard decisions. No more moral anguish about what is right or wrong or best for as many people as possible.
No more sacrifice. No more choices to make. No more mistakes to learn from. No more possibilities to discover. No more stories to write.
And that's exactly what she's offering to take away for/from our player character. Whether that's a blessing or a curse is up to debate. But I think Sybil achieving her goal is a parallel to what happens if we try to cheat our way out of consequences by giving ourselves all traits - the power to save everyone.