If banning them outright seems like too extreme a solution to be politically palatable, here's another option: Reclassify semi-automatic rifles as Class 3 firearms.
That would mean that someone wanting to purchase an AR-15 would have to go through a background check, fingerprinting and review by an official from the Bureau of Alcohol, Tobacco, Firearms and Explosives -- a process that takes anywhere from 12 to 16 months. And since Class 3 weapons can't be purchased by anyone younger than 21, it would solve the issue of emotionally unstable 18-year-olds buying them.
A Class 3 firearm reclassification would also make those who are approved to purchase these weapons subject to an annual check that they are complying with federal regulations regarding secure storage of the firearm, and to confirm their licensing and other paperwork is up to date. All of these hoops and hurdles are sure to reduce the civilian demand for these weapons.