Most colleges actually do track this metric - generally it's reported as "first-generation students." (Generally defined as parents without a four-year degree, not parents with zero college education, but same concept.) Here's Harvard's press release for the class of 2026, saying "Students who will be in the first generation of their family to graduate from a four-year college or the equivalent represent 20.3 percent of this year’s admitted class."
https://news.harvard.edu/gazette/story/2022/03/harvard-to-ex...
This is true, but also doesn't conflict in any way with the 20% first-generation statistic. After all, the corollary of "20% first-generation" is that the vast majority of Harvard students do have one or more parents with a college degree.