When referring to actual barbarians, the description of the barbarians seems to lie by omission--even if all the things described above are mostly true, the barbarians have wrecked their economy because central planning doesn't work no matter how many orders they give, burning people at the stake is bad for investment, their belief in an afterlife is associated with other beliefs that prevent them from making or even efficiently using scientific advances, and their inability to have sane discussion means they can't make tactical decisions or really plan anything well at all. (Etc.) That sort of thing is pretty much the reason that the West hasn't been conquered by Muslim fundamentalists yet:

Also, barbarism doesn't arise at random. Some social structures are more conducive to barbarism than others and they may have inherent flaws which reduce the efficiency of conquest even as their encouragement of barbarism increases it.