Another note: the cycle is not a perfect one. At the end, timeskip Shio still fails to understand why Satou sacrificed herself. So her state of mind is in some sense different from Satou's. Also, if Shio were to perpetuate the cycle, it would necessarily have to occur through a different mode of projection: Satou had no one, so she discovered Shio, who became the object of her obsession. But Shio already had Satou, so any new obsession would likely be the result of her projecting Satou onto someone else.
It's interesting that Shio's idealism is in a sense even worse than Satou's; Satou's sacrifice at the end was her one heroic action and could only be motivated by love. Shio not understanding this implies that her vision of love is yet shallower than Satou's, twisted as it was.
I think the series has a lot of sequel potential, considering the state we leave Shio in. Maybe there is a path towards healing, because in the end, Shio is simply a victim, and a pitiable one at that. We see in the original hints of better possibilities; Shouko offered virtuous love, but ended up failing due to circumstance. Even Satou recognizes this in some sense; Shouko's death is a turning point and we see that it is greatly regrettable even for the twisted Satou. So in a better world, for this love story, there might be someone out there to truly model love for the now grown-up Shio.