In a very captivating introduction 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 elsewhere on MO. I have a more neophyte question: what are practical examples of studying such simplicial complexes, and do any deep combinatorial results stem from this equivalence?