the term assault rifle was first used during WW2
sturmgewehr is german for "assault rifle" and the stg44 (actually designated mp43, for Maschinenpistole, to trick hitler as he was not keen on the new assault rifle and wanted them to develop sub machine guns instead) was designated "sturmgewehr" and it was hitler himself that came up with that term.
the "assault rifle" term ion the 70s was coined by the anti gun movement to make them sound evil but has been around a hell of a lot longer time than that.
assault rifle does not actually mean what it sez in that link (yep its a dictionary but it is technically wrong in this case) as an assault rifle must use an intermediatery sized cartridge to be termed as syuch. eg the m14 and FN FAL are as websters described " any of various auto or semi auto rifles with large capacity magazines for military use" but they are not assault rifles they are battle rifles as they use a full sized rifle cartridge (both 308)
also its arguable whether they have to be military rifles
aslo it does not apply to machine guns as they are not rifles. the assault rifle in game we have by weight especially and by looks really should be a LMG (LMG not machine gun as it uses the lighter 5.56 cartridge)
the modern (well ish) assault rifles such as ak47, ar10, m16, fnfal etc etc were not designed for looks nor were they designed based on the idealogical and art deco of the time but for functionability
WW2 unlike WW1 the battles were at much closer ranges were the power of a big heavy cartridge (such as the .303 and 30 06) was unnecessary, which is why the germans developed the stg44 with a shorter lighter cartridge. This allowed the troops to carry far far faaaaaaaaaar more ammo on them but also due to less recoil and muzzle climb due to the lower powder charger a much faster and more accurate fire rate while still maintaining a much heavier hit impact than the pistol cartridges that the sub machine guns used..
the ak47 was developed based on the stg44 (despite kalashnikov denail of this you can clearly see the similarities). The russians who were on the receiving end of the stg44 the most were very quick to adopt this lighter cartridge as they learnt the hard way how good this was.
unfortunately the other allied parties were not convinced, especially the americans, and prefered the old school big heavy shock cartridge so when NATO was formedto oppose the soviet block they adopted a full sized rifle cartridge the 308 as their standard round and the assault rifles were developed around that such as the G3 FN FAL and american M14
it did not take long for them to realize this and is why the 5.56 Nato round was developed originally 55gr and was then replaced with the SS109 round which was heavier bullert at 62gr
the development of rifles and rounds in our world is based purely on how they perform and the ability of our soldiers to wield and use, it has absolutely nothing to do with looks and/or art (only if psyhcological such as looking down the big fat wide barrel of a 12gauge pointed at you) and there is no reason to think that wouldnt be the same in the fallout universe.
the only difference between our world and fallout is in their world technology grew exponentially against ours and their mindset for art/culture/lateral thinking etc stayed in the 50s mindset (such as smoking is good for you, better dead than red etc)
they are still the same human beings as us so therfor have the same strengths and weaknesses, the ability to fire at faster rate more accurately and to carry more ammo per troop is just as important to us as it would be to them so weapon development would have parralled ours just at a much high tech rate.
the big heavy clunky assault rifle we have in fallout 4 goes against every design logic, the only explanation is power armour and yes i agree thats a good explanation but not when you think about non PA troops, police forces, BADTFL(?) agents, recon etc etc where that weapon would be an utter nightmare for them. not every troop had PA.
what they should of had is yeah ok the assault rifle we have (should of been a LMG though really) and a more real world assault rifle. that way theres one for PA uses and one for those that dont and both the likers and haters of this weapon could be happy.
the m16, which ofcourse the M4A1 is a derivative of, was in tactics but i hear that apart from main story plot that its not considered canon
it is not exactly stated the exact date our timelines split but due to the fact they are 50s inspired with art/style/mindset i personally like to think of say 1959 is the split purely because our 1950s and their 1950s are the same and they must have split afterwards if its the same as ours (subjective just my opinion based on that)
so american weapons developed in the 50s
ar10 1956
m16 1956 (as the ar15, the ar15 finished final development 1958 and didnt become "M" untill adopted into military
m14 1945 started development as the t25 finished development for the model we know as m14 1956
m60 (machine gun not AR but anywyas) 1956 (this is really what should be used as an AR by PA wearers)
the m14 and the m60 entered american service before 1960
even with the disputed "when did timelines split" we do know for a fact WW2 was same in both worlds and the m14 is a development of the m1 and the m60 a development of the mg42 german WW2 machine gun. Also ofcourse every single designer behind these rifles was around during the second world war and theres noi reason to think that they wouldnt of done what they did in our world as in the fallout world.
personally i think they should of kept continuity between the games, it doesnt have to be real world weapons as although the R9, sniper, 10mm submachine gun, combat shotgun etc of fallout3 were based on real world weapons they are not real world weapons but fit in perfectly with the previous fallout games. (especially the 10mm sub as it was in those games)
im really unsure though as to why if they wanted to go with old school almost steam punk style like weapons (fallout is not steampunk) why they didnt have both those and more real world style weapons too, probably would have kept everyone happy?