Of course it is, but the point is that it's silly to portray a fictional future that has no popular culture less than 300 years old. It doesn't matter how convincingly futuristic it is -- the point is that it's far more unconvincing if it isn't there at all. The phenomenon you're mentioning can date a show or movie in retrospect, yes, because the "future" music will sound backward to viewers a decade or two later. But the phenomenon I'm talking about dates a show immediately, because the cutoff in popular culture is so obviously the present day when the show is made. Picard likes 1940s detective stories. Tom Paris likes 1930s movie serials and 1950s cars. Bashir likes 1960s spy movies and Vegas singers. Kelvin Kirk and Jaylah like 1990s heavy metal or punk or whatever. But nobody ever likes anything from the 2000s or 2100s. And that is egregiously artificial, that absolute cutoff corresponding to the date the show was made. It's ridiculous. I'd rather have future music that sounds dated in 20 years than no future music at all.
After all, the technology and costumes and social mores are going to be just as dated later on, so that's no reason not to include them. All a science fiction story can do is extrapolate forward from the present as best it can. The fact that those extrapolations will seem dated to future generations is simply a standard occupational hazard.
And again, I am not talking exclusively about music. I'm talking about any and all pop culture -- books, movies, serial fiction in whatever form, games, sports, fashion, you name it. (Sports is the one area of pop culture where Berman-era Trek did attempt futurism, with things like Parrises squares, Velocity, anbo-jytsu, and futuristic tennis rackets and racquetball courts.)