I'm pretty sure that the singularity is not the fact that it's a point, but that the gravity is so high that it wraps in on itself. i.e. that spacetime has a hole in it.
I know Wikipedia isn't a good source for physics, but:
"While in a non-rotating black hole the singularity occurs at a single point in the model coordinates, called a "point singularity", in a rotating black hole, also known as a Kerr black hole, the singularity occurs on a ring (a circular line), defined as a "ring singularity". Such a singularity may also theoretically become a wormhole."
I know Wikipedia isn't a good source for physics, but:
"While in a non-rotating black hole the singularity occurs at a single point in the model coordinates, called a "point singularity", in a rotating black hole, also known as a Kerr black hole, the singularity occurs on a ring (a circular line), defined as a "ring singularity". Such a singularity may also theoretically become a wormhole."
http://en.wikipedia.org/wiki/Gravitational_singularity
It seems a singularity is either a point or a line, but never a sphere for example.