Each statistical tests comes ...

Each statistical tests comes with certain pre requisites and normality test is one of the key prerequisite. If the data used is not normally distributed then the further test you conduct basically loss its power. It is like a Pre Qualification before you qualify to work for certain field. Like a Degree. So normality test is must. If data is not normal, you require to transform data to various forms like log or others and check whether the normality of data is improved it or not. 

Try to run Linear regression on non normal data directly and transformed data . You will see the difference in the results you get. Indeed there are certain tests still available which are performed on non normal data like Z test for t-tests where Z test is used for non normal data.