At our gup testings, I ask the yudanja on the testing panel to be prepared to do a demonstration at the end of the test. The reasoning for this is two-fold: it is a treat for the gup students to see the leaders of the class in action, and it gives the black belts an opportunity to display what they are focusing their training around.
Each time we do this, it is met with what I can only describe as dread. No one is particularly keen on this concept (except me) and no one ever seems to know what to do.
On one hand, I'm very grateful not to have the opposite problem: a bunch of show-offy black belts who fight over the limelight. The last thing the world needs are more martial arts prima donnas.
On the other hand, it is a difficult line to tow with my students. In traditional martial arts training, humility is constantly ingrained into us. We are always told that there is room for improvement, that we only understand a small amount of what is out there, that Cho Dan is where the "Real Learning Begins." If you follow that premise, what can you possibly have to offer?
In my (humble?) opinion, it is these opportunities to explore and demonstrate that make us real students of the martial arts. Once we reach 1st dan, we should have a good grasp of the "rules" of martial arts. Our career is then spent refining those techniques, making them stronger, and suit them to our working understanding of the art.
These opportunities are those moments for growth. Not the demo itself, but the preparation and the study that goes into a demo. As you learn more, perhaps you are sent in a comletely different direction. Say you wanted to do a "simple" demo and showcase a hyung you are working on. Perhaps you might do some research into that form, learning more about it's history and the intent of the movements. You might look to other arts to see stylistic differences. Maybe you experiment with the tempo, do it backwards, mirror image, turn it into a 2 person fighting drill. Either way, being forced to do the demo led you in directions you may have otherwise not followed.
Master Homschek credits an instructor's demo using a belt as a weapon for the basis of his entire flexible weapons curriculum. It started with a belt, moved into hapkido, filipino arts, chain whips, bullwhips, neck whips, bandanas, etc until he was able to conceptualize it all into a complete system of movement.
That particular instructor, as smart as he is, probably didn't envision the following events. But he inspired a student, which is the eventual outcome I am seeking from these demonstrations.
Note: The pictures featured are from the 2002 WTSDA World Championships. At each world championship, individual Masters present one of their specialties to the audience. They didn't just get to that point, they had to practice - publicly and privately -- a lot.