The Harvard documents answer this and related questions for us.
For white admits (% of total):
Development/Dean’s Interest – 14%
Legacies – 22%
Recruited Athletes – 16%
Faculty + Staff Child – 2%
Overall (considering all races):
Development/Dean’s Interest – 9%
Legacies – 14%
Recruited Athletes – 11%
Faculty + Staff Child – 1%
If you run the numbers, this means that at Harvard, 54% of the white admits are chosen from just 9% of the white applicant pool.
Including all races, 35% of admits are chosen from just 6% of the entire applicant pool.
Yeah, I think a lottery might work a bit better in terms of assembling a better group of students, so long as Harvard set a floor qualification (GPA + scores). Sure, a few spectacular candidates might be missed, but when you are taking such a large proportion of the class from such a small subset of the applicant pool, by definition you are excluding many of the most promising candidates anyway. Holistic is simply a smokescreen to mask institutional goals under the guise of picking an optimal class. Again, there is no evidence that adcoms know how to pick optimally anyway (this is an almost perfect analog to the active vs. passive management debate in finance, for those who are familiar with the question).
I myself favor a mixed approach: 20% chosen on whatever bases the school wants (consistent with law) and the rest lotteried, subject to a floor qualification.
(All numbers are approximate and taken Arcidiacono Table B.3.2 in the initial expert report. The numbers are slightly different in the equivalent table in the rebuttal report, but only because athletes are excluded in the latter report. See p. 112 here: http://samv91khoyt2i553a2t1s05i-wpengine.netdna-ssl.com/wp-content/uploads/2018/06/Doc-415-1-Arcidiacono-Expert-Report.pdf.)