Q:   Why does it matter whether the short circuit solution is linear or nonlinear?

A:   The solution of linear systems can often be found directly by solving a system of linear equations. Many convenient theorems, like the Thevenin and Norton equivalent theorems, can also be applied in linear networks to simplify the calculations.  Nonlinear systems usually cannot be solved directly, and iterative methods are usually required to find an approximate solution. It is possible that an iterative technique may not be able to find the solution even if a solution exists for a particular network fault condition.