Forgive my ignorance, but regarding the music you linked, is it diegetic? Does it exist in the universe of the game itself, with your player hearing it, or is it ambience that is only heard by the player, existing outside the world?
If it's the latter, I kind of think that's missing the point, because I think most of us are talking about diegetic music that the player would hear on their Pip-Boy, similar to pieces like "Big Iron" and "I Don't Want to Set the World on Fire" in previous games. I know I'm not advocating Elvis being played in a non-diegetic fashion, but I do think his music would be something that would be played by the likes of Three Dog or Mr. New Vegas, and presumably whatever other DJ we learn of in Boston.
If it is diegetic music, is it Old World or New World music? If it's the latter, then of course it isn't going to sound like the songs of the 50s. It's from a post-apocalyptic society that survived nuclear annihilation. The Great War completely changed the culture of the world and would obviously have an effect on their arts, music included.
Non-diegetic music, that is to say the soundtrack that plays when exploring the world, should reflect the atmosphere and tone of the post-Great War America. But tell me why the music being enjoyed and produced in 2076 wouldn't sound like stuff from the 50s, when the rest of the culture of Pre-Great War America is locked in that time, outside of blending what was then thought to be the way of the future? You say that the youth would be listening to whatever they thought the future music would sound like because they wouldn't want to embrace the stuff that came before them, such as their great grandparents music. But then why are they okay wearing the same fashion as their great grandparents? The music being the only thing that changed to reflect the 120 years between Fallout's aesthetics and the end of the world as they new it is more ridiculous than the culture being practically locked into the 50s.
And going back to something I said earlier, your complaints about some things are exactly why I said Bethesda should write some original songs, from both the Old World and the New World. It helps avoid licensing issues for one thing, and for another it makes it so that it wouldn't be a universe of only cover bands.