looks like you have summarized it well. Could actually competing too much with a pro hurt am leader or am follower? when we dance with our teachers during the lesson everything comes so easy, so if we both compete with a pro, could we loose the balance in am/am partnership?
But when competing with the teacher becomes a goal, you are likely to each embark on private projects with your teachers that your partner won't (and quite often shouldn't) be in a position to support when you dance together. Some of that will simply be to take advantage of the pro's capability, but some will also be that pro-am can (not always, but easily) become a bit over-the-top with certain aspects of dancing ending up out of natural proportion to others.