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...
Yale doesn't report this statistic as far as I could find, although I found a blurb that says "more than one out of every six" (https://admissions.yale.edu/advice-first-generation-college-...).
Princeton's class of 2025 was 22% first-generation (https://www.princeton.edu/news/2021/04/06/extraordinary-year...).