The question then boils down to,
"What features does an assault rifle have that differentiate it from other weapons and when are those features useful to the average American?"
Assault weapons are typically rifles with specific features, including semiautomatic fire and magazine ammo storage. In addition, as gas pointed out, they must have a few other features, such as a folding or telescoping stock, a pistol grip rather than a rifle grip, a barrel shroud, provisions for a silencer, etc.
Each of these things take a normal rifle and make it easier to fire multiple rounds quickly and to conceal it. The barrel shroud ensures that even if you fire a dozen rounds, you won't get burned by the barrel. The folding stock and silencer allow you to more easily hide the weapon, or your use of the weapon. The pistol grip and forward grip make it easier to control the weapon without steadying it against a shoulder or using a mount.
The only time in recent history when I think someone would have a valid reason, according to your particularly narrow definition of need, to have wanted one is if they lived in new Orleans during and shortly after Katrina hit. The mere sight of an assault rifle would have sent scavengers skittering away, and it would be relatively trivial to scare them away further by shooting multiple rounds in a way that wouldn't hit or hurt them but would cause them to rethink their plans. This would work even for those scavengers carrying guns, rifles and even assault weapons. In a situation where there is no authority or law, the person with the most frightening looking weapon wins. You would not get the same response from a rifle, shotgun, or handgun.
Yes, there are lessor weapons that often meet the needs without having the all in one design that an assault weapon provides. If you think that this is a problem, then you must also agree that no one needs an iPhone or android phone, and instead people should carry a music player, a video game machine, a cellular phone, a PDA, a laptop, and a 3G Internet router with them rather than combining many of the strengths of each product into one device.
Keep in mind that fully automatic weapons are a completely different class altogether, and they are heavily restricted and licensed. Assault weapons are NOT fully automatic. Fully automatic weapons do not fall under the assault weapon classification. It has been unlawful since 1934 for civilians to own machine guns (guns which fire more than one shot per trigger pull) without special permission from the is treasury department, and are subject to a $200 tax every tme they transfer ownership from one legally registered machine gun owner to another. Since 1986 no new machine guns can be sold to civilians at all. Older guns are grandfathered into the national firearms act and can be transferred from owner to owner with the tax, but no new weapons can be sold to civilians.
So let's keep this question narrow and only discuss semi automatic assault rifles.
