Why isn't coulomb's law valid for large conducting objects, even if they are spherically symmetrical?

The Coulomb’s Law is as follows

According to this law, the force between two charged objects can be calculated using the distance between the objects. If the objects are large, then it is not possible to determine the distance, r, between that object and the other object. Because, the edge of the object contain charges as well as the center of the object.

In that case, you need to separate the object into infinitesimal points, apply the formula to those points, then integrate over the large object to find the force between objects.