24 US states ban cousin marriages. No states ban people over 40 from having children. You want to equate the two but there is a line between that that you can draw, as evidenced by half of the USA doing so.
I’ve expanded on my views elsewhere in thread.
Children of first-cousin marriages have a 4–6% risk of autosomal recessive genetic disorders compared to the 3% of the children of totally unrelated parents.
https://en.wikipedia.org/wiki/Cousin_marriage
Is it eugenics now to say people should avoid conceiving children that are likely to have birth defects?
Should disabled people be blanket banned from having sex or children? No obviously not. Not really workable anyways and quite morally hazardous to put into law, as you point out.
Should people with disabilities ought to (in a moral sense) have children that are at high risk of sharing their disability? Also no. To be frank, there’s a reason we call it disability. Even though they can have good, rich, valuable lives, they much more often don’t.
This is definitely a question of degrees. Society and medical support can change this line. Like where diabetes used to be a death sentence now it’s serious but treatable. So less problematic to pass on diabetes today vs 200y ago, but why would you want to?
Finally let’s get to cousins. Beyond the additional risk that they have children with health problems, there’s a question of consent. Even between cousins (like siblings) there’s often a power dynamic that makes consent hazardous. So IMO, obviously immoral. Making this illegal is not very restrictive (it affects you banging like 0-100 specific people out of literally billions) and codifies what was a taboo anyways (which is like, a pretty significant amount of law). 24 US states agree with me.
Siblings definitely have power dynamics that make consent very hazardous. I’d argue first cousins also have such dynamics. Perhaps to a lesser degree, but there’s no real benefit from having cousins marry and there is an increased risk of birth defects, so better to disallow it.
So that’s why it’s a marriage ban?