It's my understanding that many inverse-square laws can be explained as a central point emitting "interaction rays" in all directions equally. And that when another object with some area is "impacted" by those rays, it will then feel an effect proportional to the amount of rays that hit it. This amount can be found geometrically to be the inverse-square of the distance between the objects.
These laws are often used to predict the behavior of tiny particles like electrons, protons, etc. Some of these objects are sometimes conjectured to be point particles.
But then they would have no area. Which means that no matter how close or far they were to the central emitter, they would only ever be hit with a single ray. And the inverse-square law would not be observed. Interaction would be the same at all distances.
Does this mean that particles that follow inverse-square laws cannot be points? That they must have some non-zero area, no matter how 'elementary' they may be?