It's because they didn't want to date the show by having them listen to more contemporary stuff. They figured that by using things we already considered classics, it would seem less dated than having them listen to Queen or something.
Somewhat backfired, because it made the audience think they were snobs.
I never really liked "Pale Moonlight" all that much, myself.
I always figured it had more to do with Parmound being cheap pricks and not wanting to clear music. Isn't it kind of strange how the only time you hear popular music in Star Trek are in the time travel movies like Star Trek (2009) or First Contact.
Maybe it's also an issue of trying not to appear overtly contemporary. But I would think that at least one person by the 24th century might still be a Depeche Mode or Queen fan, maybe?