The fact is, most traits that we breed plants and animals for - size, muscle mass (or seed mass), fat or oil content, etc. are also polygenic traits that are influenced by environmental factors. As a result, heritability is not perfect, i.e. not = 1.0, and you get regression to the mean for exactly this reason.
That doesn't change the fact that these polygenic traits influenced by the environment are nevertheless heritable. As I recall, the heritability of fat content in the meat of pigs is actually lower than the heritability of IQ, but that didn't stop people from breeding fattier pigs for bacon. What this means is that despite the input of environment, and despite multiple genes with weird dominance and epistatic effects, you can still select (consciously or not) for higher or lower IQ people through eugenic or dysgenic behavior.
Incidentally, one of the best discussions of IQ heritability and its implications for both within and among-group (including racial) achievement is How Much Can We Boost IQ and Scholastic Achievement by the late psychologist Arthur Jensen. It's more science-based and less polemical than The Bell Curve, which is also worth reading in its own right.
Your comparison of human intelligence to livestock breeding rests on two fundamental errors.
First, you ignore the difference between individual heritability and group differences. Heritability coefficients derived from stable, affluent environments cannot be extrapolated to explain group-level achievement gaps across vastly different historical and socio-economic contexts.
Second, you treat human culture as a passive biological output. The historical rise and fall of civilizations—including those of the ancestors of modern Europeans, who were once viewed as “primitive” by imperial standards—proves that civilizational “success” is an institutional and environmental phenomenon. If intelligence were a fixed biological “stock” like fat content in pigs, the power map of human history would remain static. The fact that it shifts proves that humans are not livestock; they are highly adaptive agents whose cognitive expression is shaped by the quality of the institutional “software” they occupy.
Btw, regarding Jenkins, the central failure in the work of both Jensen and the authors of The Bell Curve is the ‘heritability fallacy’: they assume that because a trait is heritable within a population, the differences between populations must also be genetic.
This is a logical error.
Heritability estimates derived from twin studies in stable, affluent environments simply do not translate to group-level differences caused by vastly different historical, nutritional, and educational environments. When you strip away the social and institutional ‘software’—as Jensen’s work famously did—you aren’t measuring ‘potential’; you are measuring the state of the subject at a single, static point in time.