In a very captivating [introduction][1] to discrete Morse theory, Robin Forman makes the following remark:

> ...However, that does not explain why so many simplicial complexes that arise in combinatorics are homotopy equivalent to a wedge of spheres. I have often wondered if perhaps there is some deeper explanation for this.

The latter enigma seems to have been [addressed][2] elsewhere on MO. I have a more neophite question: what are practical examples of studying such simplicial complexes, and do any deep combinatorial results stem from this equivalence?

  [1]: https://www.semanticscholar.org/paper/A-User-s-Guide-to-Discrete-Morse-Theory-Forman/95e96a06d60204d271c3e144c3c2f915283f1168
  [2]: https://mathoverflow.net/questions/17370/why-do-wedges-of-spheres-often-appear-in-combinatorics