Flooding Minakami village is all it takes to keep the Abyss from spreading but they didn't do that.
There's not actually any confirmation of that, though. A lot of people speculate that it's the case, and I've seen some people suggest that the Repentance was a one-time deal rather than a repeating one, but nobody knows for sure. Since the in-universe timeline has only advanced two months since the end of FF2, we really have no idea whether the flood has neutralised the Abyss.
However, this is drifting a bit off-topic. If people want to discuss usefulness and aftermath of the rituals in all the games, I could move this to Misc. Fatal Frame instead?
However... O'm more inclined to agree with Kouta... There never really WAS a real need to perform these rituals and they were just based on old tribal superstitions. The resulting curses portrayed in the games were nothing more than vengeful ghosts seeking thier revenge on the world for thier real or perceived wrongs done to them.
Like Yashuu said, I think this would be interesting to explore in future games, but it doesn't seem to mesh with the endings very well. With the exception of Spirit Camera, which is an odd one out in many ways, the endings always require completing the ritual successfully to lift the curse. The final battle with the antagonist isn't about laying them to rest, it's about buying time to finish the ritual.