Admission to Harvard isn't a prize or reward for having good test scores and a high GPA.
There's inherent value - both to the institution itself and to the educational community - in an institution of higher education having a student body that is highly diverse in many dimensions. Those dimensions include things like ethnicity, economic background, activism, political beliefs, religion, etc. Harvard has so many incredibly well-qualified applicants that it can afford to curate its student body as it sees fit.
Medical schools are well-known for this. Underrepresented minorities tend to get accepted with significantly lower stats than whites or overrepresented minorities such as east Asians. There are good reasons for this. One, it's rather easy to do since only about 45% of people who apply to medical school get in. The schools are flooded with exceptionally well-qualified students who simply don't get in anywhere. Two, since the population of physicians is so tightly controlled, it takes this kind of coordinated, deliberate action to make sure the national pool of physicians is properly diverse (which it isn't).
Removing race and ethnicity indicators from the applications may help make admissions more race-blind, yes. My point is that isn't necessarily a good thing. Neither Harvard nor our nation are well-served by making the campus more homogeneous.