I know analogies have their limits, but would you feel comfortable if I told you I let my kid in the operating room during your procedure to do something simple?

I believe the only absolutely correct answer to these kind of questions is "it depends." As everybody pointed out, situations such as this when properly supervised it is safe, encourages further learning. However this all depends on the extremely good judgment of the supervisor....

For example, I would never let ANYBODY in a sterile area that wasn't properly instructed and observed closely in proper technique, as a kid could touch something and not tell you and the patient could get an infection. Kids are unpredictable. That being said, I would probably let an interested teenager in the (nonsterile) control room to watch a procedure from afar, and learn what I do.

However, I would argue by letting this kid on the microphone, this guy showed somewhat poor judgment; the kid could probably repeat things but

1. Everything is being recorded, and broadcast all over the internet. Honestly, what do you think would happen?? LiveATC will see a bump in traffic thanks to this.
2. No matter what you think, you have to realize that other pilots might wonder what is going on and be uncomfortable with this. A pilot does not know immediately that the controller is right behind them all the time or know that you are a responsible supervisor.
3. You'd have to really, really watch what the kid says and make sure everything is ok. This demands a great deal of additional concentration.

His "sound judgment" should have predicted national news would happen when laypeople heard the recordings. The average joe doesn't know how dangerous this is in fact, but it sounds extremely dangerous. Now, I fear an over-reaction, and legislation may ruin things for everybody else.