While not a "black belt club" we have special training for our "hit team" high intensity training team. It's an extra twenty bucks a month if you want to attend, and is geared towards the sport aspect of TKD, extra patterns and sparring practice for tournament competition.
While hit team participation does not necessarily affect the speed at which students are promoted, those students that choose to attend are typically more motivated than those that only attend the regular classes. Not to mention, the extra hours they spend training makes a big difference in how quickly they improve.
We have something we call a black belt club, however it's intention is strictly motivational. Typically when a student reaches red belt, a parent or other family member, pays for the students membership in the black belt club. For 30 bucks, the student gets their embroidered black belt which sits on a display shelf in the dojang as an incentive to help them through their next year or more of training.
Frankly, I don't see a problem with providing different opportunities of training, and asking that students pay for those extras. If the instructor is going to take more of their time to teach them, they should get paid more.
Oh I'm sorry, I keep forgetting that MA instructors are not allowed to make a living teaching, unlike every other kind of instructor in our society. How silly of me.