Beyond a "cool fact", this is the only reason that physics works, where I'm defining physics as the human study of physical laws, not the laws themselves. If we couldn't neglect higher moments systems from planetary motion to the large scale structure of the universe would be computationally intractable.

And it's not just gravity, it's also electromagnetism: charge arrangements (i.e. ions) look like point charges at a distance, meaning you can neglect the electron orbital structure. Light sources act like point sources at a distance too.

A lot of the equations you learn in introductory physics rely on the higher moments vanishing.

- The planetary motion equations (Kepler's laws) assume gravity as a point source (the three body problem can be approximated by replacing two of the bodies with 1)

- E = mgh -> assumes a homogeneous gravitational field, which is a special case of gravitational monopole near an equipotential surfaced. And of course parabolic motion and pendula only work because this holds.