It's an unsolved problem on the boundary between population genetics and systems biology that in the micro-scale metabolic systems that we have been able to understand, we find that the structure is quite complex, featuring cyclic regulation networks with nonlinear interactions. It's not at all obvious why modifications to the genetic structure underlying these subsystems would result in incremental additive effects on fitness. Some breeding experiments involving unusual variants in artificial populations (fruit flies) have also seen strong gene X gene interactions. In contrast, quantitative study of fitness traits, both in wild populations such as humans, and also in agricultural livestock, mostly find strong additive heritability and little sign of gene X gene interaction.

This problem is outlined in Data and Theory Point to Mainly Additive Genetic Variance for Complex Traits, Hill08. The paper also makes an argument which appears to rest largely on neutral selection. This may indeed be a partial explanation for predominant additive genetics, but an aside about the effect of strong interaction is quite suggestive of adaptive effects that can't be ignored:

With many loci, however, such extreme models do not explain the covariance of sibs (i.e. any heritability) or the approximate linearity of inbreeding depression with inbreeding coefficient, F, found in experiments, or the linearity in response to artificial selection.

An intuitive explanation of why heritability disappears under the strong interaction models Hill et al. consider is that this interaction makes offspring fitness highly unpredictable (as long is there is any diversity for those genes).

The explanation I propose for why population genetic variance appears additive is that strong gene X gene interaction makes sexual reproduction dangerous. Sexual reproduction is only a worthwhile bet if there are strong odds that the offspring will be viable. There will indeed be intricate strongly-coupled pieces of biochemical machinery in the population, but any deviation from the consensus architecture will be strongly punished. When mating incompatibility becomes prominent, then the only satisfactory solutions at the population level are a sweep through the population or speciation. Though not exactly the same, this reminds me of the classic example that “number of eyes” is not heritable in humans, even though it is a direct consequence of genetic developmental programs. Eye count is not heritable because deviations have severe effects on fitness. A relevant concept from economics is the Network effect, where the advantages of conforming to a communication standard (sexual reproduction) leads to runaway success of particular variants which might not in isolation have any obvious fitness advantage.

I note an important interaction with evolutionary theory: mate selection. If genetics were not primarily additive, then (as shown by Hill) there would be no heritability, so mate fitness would be no indicator of offspring fitness. In this framework, there is no reason why mate selection would ever be adaptive, so could not evolve. We may not be able to explain exactly why genetics must be largely additive, but we (and most other animals) do assume that mate fitness is relevant.

If we accept that sexual reproduction requires predominant additive genetics, then this amounts to a sort of anthropic argument for genetic additivity. Any biologist will necessarily observe that his/her/(other sex) own biology is additive genetic, because without a working sexual reproduction system, you're not going to get around to evolving biology professors before the end of the universe. See Meta-Evolution, Anthropic principle.