While Babylon and Assyria were used by God to get the attention of the Israelites, one shouldn't think that they were favored by God.  In fact, once they were no longer useful for His purposes, their nations faced demise because they never submitted to Him.  In their arrogance, they sought to make themselves like gods, and so God had no choice but to humble them.  Nonetheless, God used these people to accomplish His purposes even though they were not submitting to Him.  The same can be true today.  God uses people who are not submitted to Him to teach us and to draw us back to Himself.  Our responsibility is to pay attention and to learn whatever valuable lessons there are for us to learn.