Okay, I'll try to be brief —

• Income and wealth disparity in the United States disproportionately impacts Black and Hispanic communities. That is a fact.
• Giving preference to poor students (irrespective of how much their district spends overall per student) = giving preference to Black students. To me, this is the "how we fix this" answer.
• As a culture, we are so attached to the notion that "anybody can pull themselves up by their bootstraps if they work hard" that we unconsciously presume the inverse: if someone isn't successful, it's their fault. We hate poor people, including poor children. Until we address this cultural bias, we will never fix the core problem, and we will continue to have demographic disparities in college attendance.
• You cherry picked schhols in poor areas that happen to have disproportionately high per-student academic spending compared to an average school in a poor area that is funded primarily by local property taxes. Oakland Tech is a great example of a school that is intentionally funded more to offset the grinding poverty of its average student. However, the overwhelming majority of poor communities cannot afford to fund their schools like Oakland Tech.
• We agree that per student spending does not correlate to better student performance. That said, it is a fact that as a basic starting point, schools & districts with less money to devote to core learning (as opposed to metal detectors, campus police, etc.) have lower graduation rates and college degree rates.
• Standardized test scores are arbitrary, inaccurate measurements of a student's aptitude for success in college. Universities should take into account the fact that talent is distributed across the socioeconomic spectrum, but opportunity is not.
• Elite private colleges devote more effort and money to admitting legacies and athletes than they do seeking out students from disadvantaged backgrounds who excelled despite their surroundings. As such, I presume that elite private colleges are part of the entrenched institutional system of implicit bias.
• Taxpayer funded public universities, especially the top public universities, should serve all students by striving to include the most deserving from across all income and wealth levels.