Many of the premises of this question are fundamentally wrong. The GRE is not a good predictor of university success and does not measure someone's ability to do research. You’re also ignoring the plethora of people in the opposite position, who demonstrate good skills on a day to day basis at school but test poorly or had a fluke or didn’t get any sleep the night before and did poorly on the GRE. My example is far more likely to be hurt than yours is to be helped, as universities primarily use the GRE as a filter to throw out applicants rather than a way to improve a bad application.
The GRE does little to predict research success, primarily correlates with test prep rather than intelligence or performance when one is not actively studying for the GRE, and does little to predict or explain graduate grades. It has a strong cultural bias in favor of white upper-class students, as evidenced by the fact that it punishes students who are Spanish/English bilingual as opposed to ones who just speak English (Bornheimer), under predicts the scores of Black students (Scott and Shaw), and exacerbates the effect of socioeconomic status in admissions (Pencock-Roman), further disadvantaging poor students.
Given all this, one obvious answer is "it's a bad test." A far better question is "why do so many universities in the US require the GRE"
Scott, R.R. & Shaw, M.E. (1985). Black and White Performance in Graduate School and Policy Implications For Using GRE Scores in Admission. Journal of Negro Education, v. 54 (no. 1), pp. 14-23.
Bornheimer, D.G. (1984). Predicting Success in Graduate School Using GRE and PAEG Aptitude Test Scores. College and University, v. 60 (no. 1) pp. 54-62.
Penncock-Roman, M. (1994). Background Characteristics and Futures Plans of High-Scoring GRE General Test Examinees, research report ETS-RR9412 submitted to EXXON Education Foundation, Princeton, NJ: Educational Testing Service.