I agree that there is a strong tendency toward assortive mating, like to like.
And it is based in part of female hypergamy, women only marrying a man of equal or higher status. In this regard, women with a bachelor's degree either marry a man with a similar or higher background or overlook it if he's a well off blue collar business owner. I know a female engineer who married a skilled blue collar guy who ran a construction firm. And other women looked at her like something was wrong, he doesn't have a bachelors? What is wrong with you? Finally, oh, he owns a big business, that's OK.
There is less social mixing of the classes today, so the rags to riches fairy tale pairings (maid to heir, peasant to the prince) is almost impossible today. When such distances do exist, people tend to ignore or deliberately overlook them, assuming love will find a way. In a way, that is a fairy tale, too.
A major IQ divide, regardless of education, is a serious problem and won't work unless the pair is happy with an unequal relationship ... and most won't be.
A major divide in education can be overlooked if they are otherwise similar, like the secretary with an associate's degree marrying the professor with a doctorate in the same workplace. Or the associate's degree nurse marrying the doctor.
Really wide divides in culture, regardless of which type of culture, creates problems. And that cultural divide can be because the upper class in the US has become a very insular culture, eating different foods, shopping at different stores, attending elite schools, caring about causes no one else has the luxury to give a flip about. When there is that much of a cultural divide, it only works if the incoming partner is wholesale adopting the new culture and is OK with the elitists' seeing their origins as contemptible but the newcomer as acceptable if validating their views. "I came from backward hickville and couldn't wait to get out of there. You're so smart, so educated, rational, tolerant, loving, I just had to be you. You're so right."