This answer possibly isn't at the level that you would like, but I'm inclined to write it anyway because it's a good introductory answer. In the event that that this question does merge as duplicate, I'll probably just move my answer over there (as this is slightly different than the posted answers).
First, watch this Minute Physics video as it provides a great explanation of why any rotating, disc-like object (the Solar System, galaxies, etc) tend to be roughly two-dimensional (disc-like). The bodies begin as a collection of rotating, colliding particles. Because the momentum in the $z$-direction is roughly zero, collisions among particles will conserve the $z$-momentum at zero. The preferred way for a system to do this is for the particles to collapse into a flatter distribution. However, Conservation of Angular Momentum dictates that the matter continues to rotate.
So this answers your question as stated, but you seem to actually be more concerned with why this can't be well-modeled. I suppose the unsatisfying answer is that the universe, and the matter within it, is a much more complex place than what your typical $n$-body simulation is capable of producing. The Milky Way galaxy contains 100 billion stars, not to mention other types of objects as well.