Hard for Sylvie to care about the fate of the universe when she hasn't been allowed to exist in it most her life
Sure, but she's being given the chance to exist in it now. I don't think she would ultimately want to be the head of the TVA after all she went through. I just wanted her to have a moment of reflection or a show of trust in Loki rather than treating her choice as a no-brainer. That's all.