You cannot delete the Default shader, you can only detach it from all or selected objects. 
- In the Scene browser, expand the Shaders folder and right-click Default shader. 
 
- Select Detach Default shader From All Objects from the context menu. 
 
To remove the object so that it reveals only the other effects applied to it:
- Select the object and right-click the Default shader in the Scene browser, but select Detach Default shader from Selected Objects. 

Edge Cartoon shader A. With the Default shader. B. Without the Default shader.