This is fair; I didn't really cite anything for this claim, but it's pretty well accepted. The University of Michigan (undergrad and law school) had a couple of cases go to the Supreme Court about affirmative action and consequently put together lots of research to defend its position [0].

Some specific research on the educational benefits of diversity [1] ---

White students with the most experience with diversity during college demonstrated:

- the greatest growth in active thinking processes as indicated by increased scores on the measures of complex thinking and social/historical thinking (confirmed in the MSS and IRGCC studies);

- growth in motivation in terms of drive to achieve, intellectual self-confidence, goals for creating original works (confirmed in the CIRP study);

- the highest post-graduate degree aspirations (confirmed in both CIRP & MSS studies);

- and the greatest growth in students values placed on their intellectual and academic skills (confirmed in the CIRP study).

...

Students who took part in the IRGCC as first-year students, compared to a matched sample who did not participate in this program, showed greater growth over four years in active thinking, stronger citizenship engagement as seniors, greater acceptance of difference as compatible with societal unity, greater growth in perspective taking, greater mutuality in orientations toward their own groups and toward other groups, and greater understanding of conflict as a normal, indeed healthy, aspect of social life.

A bit about the legal system and the SAT [2] ---

A 1987 report of the Michigan Supreme Court, reached the same conclusion, noting that "the presence of minorities in the profession increases public perception of fairness." And a 1998 report re-affirmed that position, stating that by "reflect[ing] the diversity of the constituency it serves," the justice system avoids "[t]he appearance of bias, as well as the reality of bias."

...

For example, the SAT measures only about 18 percent of the factors that determine freshman grades. Even that small predictive value decreases over time. SAT scores are thus less predictive of sophomore grades, even less predictive of graduation rates, and even less predictive of professional success.

A warning and a reality check [3] ---

The impact of race-neutral admissions would be especially drastic in admission to professional schools. The proportion of black students in the Top Ten law, business and medical schools would probably decline to less than 1 percent. These are the main professional schools from which most leading hospitals, law firms and corporations recruit. The result of race-neutral admissions, therefore, would be to damage severely the prospects for developing a larger minority presence in the corporate and professional leadership of America.

...

By the year 2030, approximately 40 percent of all Americans are projected to be members of minority groups. More than $600 billion in purchasing power is generated by minorities and more than one-third of all new entrants to the workforce are persons of color. In this environment, a diverse corporate leadership can be valuable both to understand the markets in which many companies sell and to recruit, manage, and motivate the workforce on which corporate performance ultimately depends.

---

The idea here is that postsecondary education is really the gateway to power and prosperity in the US (sure there are other roads, but at a high level this is true). If we only use test scores--like the SAT--we'll shut out racial minorities from the process. The consequences of this is that education will suffer, our businesses and markets will fail to serve racial minorities, and faith in institutions will weaken as racial minorities are barred from the educations that will give them access to economic prosperity and impactful roles in our society. Furthermore, diversity is great for education for every student, not just the direct beneficiaries of affirmative action.

[0]: https://diversity.umich.edu/admissions/research/

[1]: https://diversity.umich.edu/admissions/research/expert/gurin...

[2]: https://diversity.umich.edu/admissions/research/expert/intro...

[3]: https://diversity.umich.edu/admissions/research/expert/bowen...