In addition to Mark's answer, we also have reasons to expect a spherical distribution.
The following makes some assumptions on how our solar system formed. They are standard, but we are not completely certain on its correctness. What I use is usually considered noncontroversial--it's how the planets themselves arose that is most problematic, but is not needed here.
Early in the formation of the solar system the gas and dust would have had a fairly uniform and spherical distribution. It is unlikely that the cloud would have exactly 0 net angular momentum, meaning it would have net angular momentum in some direction.
Now the gas that is sufficiently close to the sun will be dense enough that the particles will be interacting and colliding regularly. This causes the angular momentum of the particles to align in the direction of the original net angular momentum. This is due to the conservation of angular momentum.
This process creates the dominant protoplanetary disc you are familiar with, leaving a thin layer of low density gas and dust in the same sphere.
Low density particle distributions will be essentially collisionless. They will therefore not align themselves into a disc, whether they have a net angular momentum or not. Each particle orbits on whatever plane it just happens to be aligned on.
Now to the Oort cloud...
Get far enough from the center of the formation of our sun and the gas becomes less dense. As such the gas becomes mostly collisionless, and preferential alignment on a disc becomes less likely. Stay just close enough and sufficient interactions and random inhomogeneities arise for planetesimals to build up, each one aligned essentially independently of the others. They remain sparsely distributed and collisionless as a whole (basically the particles just got bigger), and so do not align.
The models you see with a doughnut-like region are ones that are expecting a region where the dust and gas was still interacting enough with itself, and the rest of the solar system as we know it, to still (partially) fall into the preferred alignment.