The bombs fell on October 23rd, 2077. Fallout may be set in a 50s-like style, but that's because it's retrofuturistic. Socially speaking, it's the 50s, but technologically speaking it's the future. Something from the 80s could exist, it would simply need to fit into the 50s vibe.
I definitely understand what you're saying. My understanding is basically how Tim Cain explained it (I'm assuming you know who that is). Fallout is not set in the actual future,
it's set in the future that people in the 50's imagined. It's technically an alternate universe. The alternate time line splits off from ours sometime in the late 50's, maybe early 60's (not to say you didn't already know that). My personal interpretation of this would mean that unless people in the 50's would have imagined this song, it couldn't exist. I guess it just depends on how you look at it. If post-50's things could exist in Fallout, then why would people still be watching black & white TV? Why would all of the music in any of the games (excluding Fallout Tactics or BOS) be from the 50's or before the 50's,
but never after the 50's? Why would there be no mention of any of the real-life Post 50's wars? There aren't any of the same events after the 50's, so how could a song written after the 50's exist?
Wow, I start typing. and before I know it I have a huge paragraph... sorry for typing so much, but thanks for reading if you did!
Also, please keep in mind I don't mean to say that my view is any better than yours. I'm simply explaining my own personal understanding of the franchise, and I don't mean to put yours down.
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