Most carbons specify .006 tolerance. Some are .003 and the real expensive ones are .001. I don't find it difficult to get wood to .006. On the other hand, wood is often bent in the field from shooting, incorrectly pulling it from targets, etc. The nice thing about wood is it will fly straight even when the shaft isn't, provided, of course, the nocks and points are on straight.
Also, wood has a tendency to shoot itself straight. If it's not bent too badly, just a bow in the shaft, for example, it will often straighten out through shooting. Doesn't always work, but does quite often. I think the flexing the arrow goes through tends to equalize the forces within the wood, thus straightening it out.