Consanguineity itself isn't the danger, it's when it's repeated over and over weeding out genetic diversity that's the problem. IRL the "Hapsburg jaw" took over a century of "all in the family" to become more than just a distinctive family resemblance. (They had other genetic issues as well.) Queen Victoria passed hemophilia to her descendents, but the hemophilia itself isn't tied to incenstuous ancestry, it's just bad luck.It also explains why their are never any birth complications or incestuous mutations/deformities no matter how many kids he has, their grandmother is a Fertility goddess so each pregnancy is blessed/protected by her.
But 100% on why the MC's (many!) kids always seem to lack any kind of birth complication. And why future generations of his offspring may mysteriously avoid genetic ancestry issues as well.