The diversity Harvard wants is the golden calf of American liberals: black Americans. Diversity is almost always code for black people. No other race seems to deserve any attention. See how campaigns like #OscarsSoWhite were propagandized as discrimination against blacks even though the percentage of black actors winning Oscars was nearly identical to their percentage of the population, i.e. Oscars were perfect representational of black people, meanwhile every other race was greatly under-represented.
A race-blind policy that factors in class/income will result in more poor asian students dominating placement, likely at the expense of black students. We already know from the discrimination lawsuits how much contempt Harvard has for asian Americans, I assure you Harvard don't want this kind of diversity.