Personal opinion ahead:
I just disregard any FO4 'design' concepts, to me, my head-cannon firmly places that the USA was using what we see now as current 'real' modern weapons there is no viable reason the technology of weapons design and manufacture should deviate too far into the Fallout timeline/universe. This is why I personally like where Fallout Tactics places the idea of pre-war technology although many might disagree on this.
(you can stop reading here, or continue for the 'full rant')
I could now spout a bunch of headcanon at you, but I'll just sum it up by saying this - FO4 aesthetics are garbage. The 50's thing being driven down your throat as though it is a FACT that America in 2077 had failed to make ANY technological progress in more than 90 years.
I realise that the FO timeline calls for a 'very late' progression to microchips, but it did happen, and so at best, modern technologies were stunted by about 30 or 40 years of growth and advancement. There is to me, absolutely no reason that in 2077 the world would be like Bethesda has chosen to portray it, they took all the kitch concept of fallout, but none of the cyberpunk or post-modern gothic influences.
Bethesda utterly disregards that (at least how I understand it) the 50's "thing" was used as a placating ploy by the government to ensure a populace that didn't outright explode into civil war. The twee and pleasing aesthetics backed by Bladerunner-esque 'hyper-technology' running behind a facade of old-timey goodness. Outside of the more affluent area's I imagine things to be more like modern day Detroit or Harlem of the 80's the buildings would look like 'normal' albeit run-down buildings that we see today, the civilian-owned tech inside them probably a heck of a lot like we had in the late 80's/early 90's.
Storyline aside, culture, design concept and growth of industry doesn't just 'stop' because of one insignificant detail. And this brings me back round to my final tirade aimed squarely at the question raised by OP:
Why does FO4 have 'old' style weapons? - Because Bethesda couldn't write their way out of a four-line soliloquy and lack the integrity (and probably the skillsets) to maintain a solid world-building lore & canon friendly game world which maintains clear suspension of disbelief.