They did that. They had an episode of Reading Rainbow where he talks about playing Geordi and shows off the set and other things from the show. It’s how I know how they did the transporter effect, as it was explained on that episode of RR! They just had some blue beads in a graduated cylinder and stirred it up. 😃
It sort of exists. In Reading Rainbow S6E1 “The Bionic Bunny Show”, LeVar gives a tour of the TNG set and explains the show production. (somewhat odd, IMDB has the episode incorrectly listed as S5E1)
Already happened; there was a Reading Rainbow episode where LeVar Burton showed the audience the Star Trek TNG set. He showed how the transporter effect was glitter stirred in a glass. It was pretty awesome to see that as a kid and it also made some connections between fiction and reality that can really help ground an impressionable mind.