The point of choosing Kevin Bacon in the first place was that "Kevin Bacon" sounds roughly like "separation," so the reference works. AFAIK there was no additional criterion.
https://www.youtube.com/watch?v=JMn3B4LAP48
They don't mention it on the Stewart performance, but they had just seen Bacon in two films on TV back to back:
https://www.nzherald.co.nz/entertainment/the-exact-history-o...
Now, maybe they named the game "Six Degrees of Kevin Bacon" because it sorta rhymes with "separation", but they didn't pick him to rhyme with the phrase.