But Moenghus the Elder, Kellhus, Maithanet, Serwa, Kelmomas.
Exactly. We have far more textual proof of the link between genetics and sorcery than otherwise. I think all we have is that Sorcery is generally believed by schoolmen to not be link to hereditary. However, most schoolmen don't have any children and aren't allowed to have wives. It would be an extraordinary coincidence if Moe Sr. was an anomaly and had (at least) 2 anomalous children from 2 different mothers who could also see the Onta. More extraordinary still that half of Kellhus' own children had the ability as well. To me, it is far more likely that the trait is genetic, rather than random.
Also note that its entirely possible the Onta perception is a dominant genetic trait. IRL left-handedness is dominant, but those who were left handed used to be killed because they were thought to be witches. Schoolmen have been hunted for centuries, and for whatever stupid reason they have not been allowed to breed very often.
Where do the Mandate recruit their members from? Oh yeah, a small fishing village right outside of their stronghold .... How convenient.