This is so interesting. Age-old preference of women for men who are savvy, educated or possess "know-how" is now likely the leading driver of US income inequality. Why? Because our modern era for the first time, permits women to work in hi-comp occupations. If their age-old preference biases them to hi-comp men, you get hi-hi couples for the first time, when in the past you almost always had a lot of hi-lo couples with the woman (unfairly) relegated to lo or no comp stations.
Think about it. Assume 10% of the jobs in your work force are hi-comp (making X times more than lo comp) and 90% are lo comp. With random mating, you end up with 20% hi-lo couples and 80% lo-lo couples. Hi-lo's would make (X + 1) / (1 +1) = (X + 1) / 2 times as much as lo-los. So about half the inequality among couples than among individuals.
Now with completely assortative mating, the half the hi-comp individuals are women and they select the other half of the hi-comp individuals who are men. Now your couple population is 10% hi-hi's and 90% lo-lo's. Hi-hi's make (X + X) / (1 + 1) = X times as much as lo-los and there are half as many of them than without assortative mating, exacerbating inequality further. Thus, income inequality among the couples in this population should increase by a factor of X / (0.5X + 0.5) / 0.5 = 4X/(X+1) ~= 4 times larger than without assortative mating .
This really turns the political discussion on its head. Democrats are supposed to be the party supporting women and opposing inequality. Sure rent-seeking fat cats are lobbying their way to tax breaks and a good citizenry should push back on that but this is bigger than the tax code and its not going away. I would be interested in examining this effect in other developed countries.
I think that because this effect is persistent and growing means it is all the more important we invest in training and educational opportunities that improve what "lo-comp" means while investing in strong public health and transportation infrastructure to buttress the living conditions of the many couples in a lo-lo type of pairing.