I found this that says that the half finished bridge is a gateway for the deceased into the world beyond. This would make sense, as it is called "Sendoff" Spring. Maybe it's the place, you know, where they do a 21 gun salute or something like that. Based on the mysteriousness of the place, and the fact that there is a half finished bridge over a cave that houses the entrance to the Distortion world, (Pokemon version of the underworld,) and Giratina, who is the Pokemon god of Death and Antimatter, I think this explanation makes sense. Bulbapedia says this too, but it doesn't specify the bridge as the gateway to beyond.
I don't think there is any definitive reason for the bridge to be half complete, but this is the best that we can do.