Maybe pop culture doesn't exist then.
Though it depends how one defines it. If it's media-driven attitudes and memes, then the media in 24th century Earth or the Federation in general may be very different from today.
Also, as the Federation is a multi-species union, not all cultures may even have media (at least as we know it or would recognise it).
Pop culture (or mass communication) today is economically and politically driven. That was true in ancient times, with theocratic and monarchial control over mass communication and ceremony, that is so in today's corporate-state society. The system only promotes itself through its communicative means. In Roddenberry's future those factors are not supposed to exists anylonger, so pop culture/consumer society (at least as we know it) shouldn't exist either. I think Roddenberry was envisioning a more creative rather than consumerist society based on mutual support and equality rather than competition.
Well, again, "Roddenberry's future" wasn't one cohesive culture that extended all through the Federation . . . and beyond. I'm sure the Andorians and the Tellarites and the Deltans and the Betazoids and the Argellians all had very different approaches to economics and journalism and art and entertainment, which would translate into different varieties of pop culture.
STAR TREK is about "strange new worlds" and civilizations, not one enlightened universal society . . . .