astrophysics - Why don't stars in globular clusters all orbit in the same plane?

Globular clusters like Omega Centauri certainly don't seem to be very coplanar at all.

In other words, why doesn't the explanation at Why are our planets in the solar system all on the same disc/plane/layer? (quoted below) apply here?

We haven't ironed out all the details about how planets form, but they almost certainly form from a disk of material around a young star. Because the disk lies in a single plane, the planets are broadly in that plane too.

But I'm just deferring the question. Why should a disk form around a young star? While the star is forming, there's a lot of gas and dust falling onto it. This material has angular momentum, so it swirls around the central object (i.e. the star) and the flow collides with itself. The collisions cancel out the angular momentum in what becomes the vertical direction and smear the material out in the horizontal direction, leading to a disk. Eventually, this disk fragments and forms planets. Like I said, the details aren't well understood, but we're pretty sure about the disk part, and that's why the planets are co-planar.

Answer

Because the stars each form from their own region of the cloud. Each star forming event is separate* from the other stars that are not in the same orbital plane. All the stars are not in a disk like the planets are. This PDF (OBSERVATIONS AND THEORY OF STAR CLUSTER FORMATION) may give you the answers you are looking for.

Furthermore, the Solar System is dominated by one single mass, the Sun, which means that to most planets, the solar system is approximately a two-body problem. This is not the case in a globular cluster, in which the stars are all of more or less comparable size. N-body systems are notoriously chaotic, so even if the stars had started out in ordered motion (which they haven't), their orbits would be highly unstable, and the cluster would quickly be relaxed into a virial system.

*notwithstanding multiple star systems that do form around each other, but this only applies to a limited number of stars compared to the millions in the cluster.