The 50s (and 40s and even 30s IIRC) tunes primarily show up when listening to the radio, which kind of makes thematic sense as the FO United States was culturally stuck in the '50s until the bombs fell. Those would likely be the only recordings 3dog and Travis would have access to, as you noted. When it comes to world BGM though, the Bethsoft titles aren't nearly as far off from 1/2, if less ambient and opressive-sounding.
Fallout is not really culturally stuck in the 50s, it is just an interpretation of the future imagined by people from the 1950s in terms of aesthetics, but culture still moved on, albeit in different ways.
Though as I mentioned there has been music in Fallout, especially New Vegas, from as late as the 90s, mentions of other famous groups in the original games, so I still don't really get why only the old records are playing apart from just strictly finding old records. My best guess is simply that using iconic retro songs were a nice introduction to the universe in the original games, but it kinda became part of the games identity since the 3D games with the radios, even though pre-war stuff was almost all destroyed. Same as the Gothic and Art Deco influences in buildings and design getting progressively replaced. There was a significant shift at some point.
It's also possible more modern music was stored on mediums that didn't survive the war, that it was censored, or simply remained part of the underground culture.
Back on topic for the thread though, I'd prefer if some smaller studio that actually cared about the lore of the original games would make another Fallout, maybe a reboot of Van Buren, or actually attempting at making new lore in different areas.
I wouldn't mind seeing a Fallout Chicago, or Fallout Texas, or Fallout North West... There are a lot of places Fallout can go thanks to th breadth of the story and themes.
Agreed, I think it would be fun to explore the same timeline on the Chinese side more...