the barbarians have wrecked their economy because central planning doesn't work no matter how many orders they give

Not all barbarians do that. The communists did that, but they also considered themselves rationalists and were considered such by many people at the time. Muslim fundamentalists generally don't.

burning people at the stake is bad for investment

Depends on whose being burned and why. Having the highest per capita rate of capital punishment doesn't seem to have hurt Singapore's ability to get investment.

their belief in an afterlife is associated with other beliefs that prevent them from making or even efficiently using scientific advances

I don't think so. It might hurt their ability to make scientific advancements, but they're perfectly capable of using them once someone else makes them.

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.

'Rationalist' societies can also have inherent flaws, like say problems solving the collective action problems associated with wars.