Bringing in "hot young bands" to play aboard Enterprise
would obviously have been implausible. But the idea of using modern music isn't inherently bad; they could have had the crew organize an "Open Mic Night" akin to the Movie Night they did use, and it wouldn't have been implausible to bring in smaller acts as Starfleet officers playing stripped-down songs on Open Mic Night.
But to make this plausible and consistent with the tone of the show, it would have been a better idea to focus on a variety of acts, and it would have also been a better idea to mix it up with songs from numerous different decades -- everything from someone playing Cole Porter to someone playing a Nirvana song, for instance. Bringing in Britney Spears to sing "Toxic" wouldn't be the best idea, but bringing in lesser-known acts like, say, Billy Bragg or Flogging Molly might well have worked -- as might have, say, bringing in Norbert Leo Butz to sing "You're the Top" or other such works.
I think that kind of flexibility would have allowed the writers to use "Open Mic Night" in much the same way the Bronze was used on Buffy
-- not only a plot device to allow the characters to socialize in an off-duty setting, but to allow the opportunity to use a variety of musical formats to explore, express, and comment on the themes of a given episode.
It would certainly have been a departure from the Berman-era Trek formula, but it might have worked on an artistic level if it had been approached from the perspective of, "How can we use the music of our lifetimes to illustrate the themes we're exploring in our stories?" first and foremost, rather than from the perspective of, "How can we get the biggest bands on the Hot 100 this week to come on the show and do cross-promotions?"