Pitch perception is logarithmic. In fact, when we talk about "pitch" as opposed to "frequency" it is usually understood that pitch is the logarithm of the "frequency. These coefficients are frequency multipliers, so their logarithms are the pitch offests (ie. they are not offsets in linear frequency). So the average in log-domain should be 0, which translates to geometric mean of 1.
ps. Whether the center of a set of detuned components is perceived exactly at the geometric mean is another thing, but it's certainly a better approximation than the arithmetic mean.