My theory has always been that culture is cyclical - it's less that society remained stagnant for 120 years, but that "retro-50's" was en vogue at the time the bombs fell. It's less that no one was ever making "new" music (or that more modern bands never existed in the timeline,) but that what you hear on the radio is what was popular. (Also - there's only one functioning radio station in the DC Wasteland, and it just so happened that it was a "golden oldies" station...
)
There's also the matter of verisimilitude, and maintaining a consistent tone and atmosphere. "Realism" will generally take a back seat to providing a concise and effective art direction in these cases. For example - in Star Trek: The Next Generation, there are Klingons that recite Shakespeare and Cpt. Picard enjoys listening to classical music. In that universe, those things still exist. It's equally possible that there's a Klingon out there somewhere with a collection of antique Gangsta Rap from Old Earth - but it wouldn't add the same sort of nuance to what they were trying to portray in that particular episode.
So I figure, if you want to stretch a point, that there's no specific reason why any specific music couldn't exist in the Fallout universe. There very well could be an ancient dust-covered CD of (well, just about anything really) buried out in the Wasteland somewhere. It's less a matter of specific things being denied by the setting, so much as it was a conscious decision of what to actually include. A selection of specifically "retro" music has a much greater impact than a variety of different music (especially considering that we're dealing with a limited number of songs in the first place...)