Typically a pro makes just as much money coaching an amateur couple as teaching a pro-am student.
In fairness, the competitions themselves can be a not-entirely-trivial income stream for some pros. That's one thing they'd get from teaching a pro-am student that they wouldn't from coaching an am couple.
That said, there is one thing I have to say. I know that there's a fairly common attitude, not without cause, that students should be fairly cynical about their relationship with their pros. That the relationship is strictly one of business and that the pros are all about the bottom line. Now, that's certainly wiser than assuming the opposite, but I think that in many cases it misses the true mark. For example, I dance both pro-am and am-am. Unfortunately, my am partner has never been willing to travel to Nashville with me for lessons with my pro, so it's very much been a case of pro-am with one instructor and am-am with another.
I found out recently that my am partner is planning on moving in the fall. It would have been very, very easy for my pro to suggest taking this opportunity to double down on my pro-am activities with her. However, she knows that my amateur goals are really important to me. Since she's of the opinion that I need someone who already has a solid background in ballroom as my next am partner, she's actively trying to think of ladies who would be good potential partners for me, and she is NOT limiting her considerations to people in Nashville. In fact, she's named one name to me so far, and while I'm skeptical that the lady in question would be interested (she really is quite a bit better than I am), that partnership would almost certainly spell the end of my pro-am days and due to the logistics of the hypothetical partnership, reduce the number of lessons I wind up taking with my pro.
In short, certainly there
are pros out there who are all about their bottom line. But there are some who really care about their students and try very hard to help them meet their goals, no matter what they might be. I'm not sure they always get the credit they deserve.