This central conceit of Trek — that humanity needs to have a good strong Etch-A-Sketch shake before it can draw a new picture — does serve a basic narrative function, of course. Humans wouldn’t have a lot of access to 20th-century pop culture if it has all been wiped out in the wars. But it also reveals that Roddenberry didn’t feel too rosy about the world of the 1960s.
Roddenberry’s utopia, it seems, was a fantasy born of turbulence. He looked around at the social strife, racism, warmongering, and petty corporate greed, and deigned to imagine a world without any of it. Roddenberry was hopeful about the future, but incredibly cynical about the present. So cynical, in fact, that he fictionally bombed the 20th century into the stone age. Total destruction was, he seemed to feel, a hard lesson we all needed to learn. Humanity would need to become a post-apocalyptic species of kangaroo courts and petty revenge before we could come to appreciate the message of interplanetary community given to us by the Vulcans on First Contact Day.
As such, any vestiges of Roddenberry’s present would have to be destroyed along with the aforementioned greed and iniquity. This meant that pop culture would have to go with it. Sorry reruns of “Batman” or “The Monkees,” or anything that came after it. You are but a vestigial outcropping of a failed humanity.
So it does sound quite odd when pop songs from the 1990s work their way into “Star Trek” vernacular. The songs are driving and energetic, yes, but every Trekkie seems to inherently sense that those things shouldn’t exist.