imo it was because in the novel khalian got interested in shavian cuz the emperor fell for him which is what happened w fl unintentionally cuz he got curious about her cuz the emperor kept hiding her so essentially khalian's interest is always piqued due to lucious obsession I think that's why rosaline never considered it plus the fact that she never considered that her brother could be obsessed with his best friend so tbh I can see why this was their best option like the trigger for world end is just shavian not the other 2 so if he's away from the two maniacs he's kinda safe but I guess fl and rosaline never thought that someone who's into crazy maniac men is also ofc a maniac like he was always a little innocent sheep to them so easiest target in their pov too like you could see they were trying to keep the emperor from meeting shavian too like it's basically dominos and they're trying to stop the first piece from falling which is the love triangle between the two emperors and the prince (this is my own interpretation btw hope it helped ╮( ̄▽ ̄)╭)

I still don't understand the logic behind making Shavian fall in love with her and how is that gonna save the world... Isn't it worst? I mean, what if he has his heart broken and kills himself? Or what if he turns into a Psycho maniac and does something really bad?
The best choice was to seduce the Emperor, it's the least bad choice, or so I think