The problem with this approach is that everyone really has to know their TNG. I have no idea what Picard said to the powerless Q. What Kevin Bacon’s character said to Niedermayer during the pledge ceremony.
It was basically an accident of history. From Wikipedia:
In a January 1994 interview with Premiere magazine, Kevin Bacon mentioned while discussing the film The River Wild that “he had worked with everybody in Hollywood or someone who’s worked with them.” Following this, a lengthy newsgroup thread which was headed “Kevin Bacon is the Center of the Universe” appeared. In 1994, three Albright College students - Craig Fass, Brian Turtle and Mike Ginelli - invented the game that became known as “Six Degrees of Kevin Bacon” after seeing two movies on television that featured Bacon back to back, Footloose and The Air Up There. During the latter film they began to speculate on how many movies Bacon had been in and the number of people with whom he had worked.
They wrote a letter to talk show host Jon Stewa, telling him that “Kevin Bacon was the center of the entertainment universe” and explaining the game. They appeared on The Jon Stewart Show and The Howard Stern Show with Bacon to explain the game. Bacon admitted that he initially disliked the game because he believed it was ridiculing him, but he eventually came to enjoy it. The three inventors released a book, Six Degrees of Kevin Bacon, with an introduction written by Bacon.
That makes more sense. It’s a historical contingency…