Thanks for the comments. There are a lot of good arguments for demonstrations as everyone has pointed out.
Nonetheless I must say that nations show off their armed forces all the time. Even animals do it as a threat display. The social display and management of force seems to be one of the more sensible things that people do.
But the social display of force is not one of them. Unless you live in a military dictatorship on the Korean peninsula. Or perhaps in prison.
The argument against budo demonstrations is fundamental and simple. In an emergency you react automatically depending on your training. If you are holding back or deliberately doing something for an audience it is by definition fake. That's why many budo teachers do not like demonstrations.