One of the most cringe-worthy aspects of The Phantom Menace was the two-heded announcer doing the play by play of the pod races. There is something about mass-media in futuristic stories that seems too, I dunno, self-reflexive? I mean, you're already watching a movie or a TV show. If your futuristic characters watch movies or TV shows, it can't help but seem too modern-day. It works sometimes, like in THX-1138 or Idiocracy, but I don't think it would work for Star Trek. I'm sure there is "news" in the Trek universe, as well as some degree of high-art (like the traveling theater companies) but not the equivalent of a 24th century COPS or American Idol.
The Fifth Element got it right. Both high and lowbrow celebrity.
ST didn't even attempt to allude to popular culture aside from some 60s music played by people dressed in tinfoil suits in the original series.