It would seem to me if every citizen knew how to properly shoot a rifle, odds are pretty good one of those things could be knocked out of the sky with a barrett.
You really put a lot of thought into this didn't you? No, the odds are far from "pretty good". There's a reason why people hunt flying birds with shotguns: the spray of pellets is much more likely to hit a fast-moving target than a single projectile, and while there are any number of people in the U.S. who are quite proficient with shotguns, only a very, very few have the requisite skill necessary to hit a bird with a rifle, much less a drone, which would probably be flying MUCH faster than a bird, and if flying low, would be in sight for only a fraction of a second.
As to your suggestion that citizens be armed with Barrett sniper rifles, it takes months of intensive training to become a proficient sniper, and they start off with expert marksmen. Even then, the very best snipers would probably be ineffecive against a target such as a drone, which, given the the advances in small off-the-shelf turbine engines that are readily available to R/C hobbyists, would be travelling at a couple hundred mph, and if flying at low altitude, would only be visible for a split second. Add to that the mass of the Barrett, which makes it difficult to maneuver quickly enough to track a fast-moving target. Plus there is the wholly unanswered question of readiness: how to alert this civilian air defense artillery corps and give them useful targeting data IN TIME to be effective. What are they going to do? Lug a large heavy weapon plus ammunition with them to work, the beach, on dates etc, on the off chance that they might be alerted to incoming drones? The idea of training large numbers of ordinary citizens to the level of proficiency required is not a tenable one, to put it charitably, and would be FAR from cost-effective.
There is also the danger of falling bullets, as another poster pointed out. And if you don't think the danger is real, tell that to my friend Cathy, whose uncle was killed about four years ago in Miami by a falling bullet. He was sitting on his back patio with his wife watching the New Year's fireworks and having a glass of champagne when he slumped to the ground dead. The first thought was that he had suffered a massive heart attack, but the medical examiner noticed a small hole near his collarbone, and the autopsy revealed that he had been killed by a small caliber handgun bullet falling from a steep angle, fired into the sky by some unknown, and unknowing, person celebrating the fireworks. The thought of masses of people firing enormous volumes of .50 caliber rounds into the sky over populated areas is a terrifying one to me personally.