I want to emphasis here some reasons why you should not stay linear too much. I can make a summary first. The most important reason is a fact that the nature is not linear system.
We assume a certain system as a linear system because of easy to manipulation but not because of its exactness. Once we can assume a system as a linear system, we can treat it easily and find a solution attached to that system.
We can say that there is a solution in a mathematical problem. However, we can not guarantee that that solution is also the perfect solution for corresponding real problem associated the natural system.
I want to present one example. Let’s consider there is a system who has multiple inputs and multiple outputs. So, we have modeled it as a vector input and a vector output system (VIVO) with a matrix system function. Do you think the natural system and the modeling equation are the same? The modeling system is one of many ways to model the natural system, not the perfect representation of the given natural system.