This question is related to this one on SE. However, I'm still not satisfied with the answers. My question can be divided as these 2:
- Is this just a convention (as Claudius said) or is there any profound reason?
- Why is $r^{-2}$ also long range? (As an example, on the P.5 of Quantum Mechanics: Selected Topics, "The centrifugal potential cannot be regarded as a short-range potential." and $V(r)=\frac{l(l+1)}{r^2}$)