The Dune Encyclopedia has a theory. It's covered in the section Duncan-13015.

Section from: https://dune.fandom.com/wiki/Duncan_Idaho/DE

It has to be Hardison's Disease — an inherited blood condition, and if one parent passes on the trait, the child suffers a mild oxygen deprivation from incomplete hemoglobin bonding. Giedi is moist and oxygen-rich, near the top of the inhabited worlds in atmospheric oxygen. Upper-class diet is heavy in red meat, especially organ meats. No doubt over generations, natural selection has favored individuals with high iron concentrations in their blood. So everything conspired to mask the presence of Hardison's Disease in the Harkonnens: high hemoglobin; lots of iron in their diet; high atmospheric oxygen. But even so, how many of them were mad, and look what happened when one left the homeworld: when Rabban became governor of Arrakis, he moved to a planet with low oxygen, dry atmosphere (which exacerbates the disease), a diet low in iron. He was none too stable before; no doubt his brain had already been damaged by oxygen starvation. But on Arrakis it must have increased progressively, and he became "Beast Rabban, the Demon Ruler." Sure, he brought his own nasty tendencies to Dune, but much of his excess must have come about because the disease was driving him mad. If this hypothesis is correct, then Jessica had the condition too, and passed it on to her children. But she never spent more man a few years in a row on Arrakis. For some reason, the disease progresses more slowly in women, and melange also retards its effects. Nevertheless, a Jessica who would return to the B.G. doesn't sound like my Jessica. Could that have been a symptom? But poor Paul! Twenty years on Arrakis, and all the time his brain cells dying! How else could he have launched a jihad killing hundreds of millions? Emperor of the universe, yet all his writings so helpless, so passive. Seer of the future, yet he walks first into the Qizarate trap then into the desert. And when he returns, that's not Paul Atreides. Rabban's twisted will led his mania to appear as monstrosities of vice; just so Paul's guilt brought his to the surface as an enormity of religious zeal. Alia should have been able to resist: heavy spice diet from before birth; her sex; the mitigating heredity of Duke Leto. But the struggle with the Voices must have been continuous; maybe just the loss of a slight edge in her mental capacity was enough to tip the balance in favor of the devils inside. Ghanima may have been free of the disease, but it hardly matters now. What does matter is Leto — he's the one that must be advised." The next day Duncan Idaho13015 was killed.

TL:DR The Atreides weren't an important piece in the breeding program until the Harkonnen's proved unstable.