I guess there's something to be said for the fact that she's so divorced from Asgard and her old identity having been taken so long (like literally every time Loki brings up something from his past Sylvie barely reacts to it) that there really wasn't anything else she would want to do.
Of course she was also very self-righteous, self-involved, and selfish to the bitter end, but I guess that was the Loki in her...while the main Loki truly evolved past that. But it did make me dislike Sylvie all the more.