I am taught that your body should learn correct posture/stance and mixing styles would seriously interfere with that. For instance, mix karate and Aikido. the stance is completely different, how would your body know what to do? Muscle memory gets confused....
And sometimes people do actually have trouble making their technique "work" as they start to incorporate IS skills. Which is probably one of the reasons why they rebel against the idea.
But I don't really think of the square posture as a "stance." More like the postural equivalent of a lab bench: a way of reducing the number of variables you need to deal with so that you can study a particular group of phenomena in their "pure" form.