Incest is probably quite bad but I don't think that incestuous marriage should be regulated.
I'd also like to point out that, along with the handful of states that were mentioned in the OP, first-cousin marriage is actually legal in EVERY SINGLE country that the posters in this thread are from (except aamirus, assuming she is from the US). Have you noticed?
I think there’s a second reason to ban it. The first reason as you mentioned: likelihood of genetic defects. Well we don’t ban people with genetic defects in general from having children so that logic doesn’t fit.
I actually think the laws come from older times where inheritance, noble families, royal families etc were more important. As a noble it makes sense to ban the royal family from incestual marriage because it forces them to marry one of you. Same with peasants and nobles. So I don’t have evidence but that’s my suspicion, because I can’t imagine why lawmakers would sit down and be like “incest is gross let’s ban it!” And not ban all other gross things or high risks for genetic defects, etc.
Have you ever heard the tragedy of Darth Jar Jar the wise?