Your original point was: "Studies have shown that the majority of women on OLD pursue the top 20% of men, in terms of appearance. The other 80% barely get a look-in."
The study doesn't talk about such percentages. It actually shows:
" although women receive more messages than men overall, the distributions for both display a classic “long-tailed”form—most people receive a handful of messages at most, but a small fraction of the population receive far more. ... We find that both men and women pursue partners who are on average about 25% more desirable than themselves ... Women initiate far fewer contacts than men, but both sets of curves fall off with increasing desirability gap in all four cities ... both men and women combine aspirational mate pursuit with less risky prospects."
So men show exactly the same aspirational dating behaviour as women.
Other interesting points:
"average desirability varies with age for both men and women, although it varies more strongly for women, and the effects run in opposite directions: Older women are less desirable, while older men are more so (18, 19). For women, this pattern holds over the full range of ages on the site: The average woman’s desirability drops from the time she is 18 until she is 60. For men, desirability peaks around 50 and then declines. In keeping with previous work, there is also a clear and consistent dependence on ethnicity (15, 20), with Asian women and white men being the most desirable potential mates by our measures across all four cities. The final panels in the figure show how desirability varies with educational level. Desirability is associated with education most strongly for men, for whom more education is always more desirable. For women, an undergraduate degree is most desirable (13); postgraduate education is associated with decreased desirability among women. These measurements control for age, so the latter observation is not a result of women with postgraduate degrees being older (table S2)."