First, it's not an
assault rifle. One of the most defining factors of an assault rifle is that it is select-fire, and there is no select-fire receiver available for it, only semi-auto or full auto. An assault rifle uses smaller rounds than a normal rifle (say, an
M1 Garand with .30-06 cal). If a rifle does use "full size" rounds, and is select fire, it is a Battle Rifle. No problem there though- the Fallout 4 Assault Rifle uses the 5.56 round, specifically developed for assault rifles like the M16. It is an "intermediate round" because it is smaller than a rifle round but bigger than a pistol round. One of the design goals of the M16 (and all assault rifles) is to be lighter and easier to handle than guns with larger rounds. Despite the M16 apparently existing (the Assault Carbine in Fallout: New Vegas*, which itself weirdly uses 5mm rounds, implying the 5mm rounds to actually BE 5.56x45mm NATO) we can tell from the design of the Fallout 4 Assault Rifle that it fulfills none of these goals. It has high range and damage, which are uncharacteristic of the intermediate 5.56mm- it basically performs like a gun that shoots full-powered rifle rounds. It is NOT lightweight- with a long barrel it can weigh to the tune of 25 pounds, which roughly matches it up to an
M60 machine gun. The M60 is a machine gun, because it uses full rifle rounds, is very heavy, and as a result
a soldier can only fire it accurately while resting it on the ground. The Fallout 4 Assault Rifle is visually consistent with this. It's enormous, has what looks like a water-cooled barrel (which should probably make it EVEN HEAVIER than what it weighs), and it also had a top grip which is consistent with machine guns, though you can't actually hold the gun that way. All it's missing is a bipod. Anyway, this heavy gun with water cooling makes sense for bigger rounds, but would be completely unnecessary for a weapon that fires 5.56mm rounds at the rate this does.
TL:DR, the Assault Rifle in Fallout 4 is a weapon which has the weight and appearance of a machine gun not meant to be fired accurately while standing up, the range and power of a standard rifle/battle rifle (depending on whether it's automatic or not), no select-fire feature, but somehow uses the 5.56 round, which is too small for what this gun does or look like. It's a complete aberration.
*To add to the confusion, the Fallout 1 Assault Rifle uses 5mm rounds, and looks exactly like the Fallout 4 Combat Rifle.