>And there are no real barriers to entry; in principle, anyone can do this
Does private schooling provide no benefit?
Private tutoring?
Family donations to elite schools?
Legacy admission?
Further:
Does food security provide no benefit to the ability to learn and retain information?
Does a violent environment offer the equivalent value as a non-violent environment, in terms of being able to focus on schoolwork?
Does a multi-parent child receive no additional educational advantage over a single-parent child?
Does having access to paid resources not offer any benefit?
Does attending better funded public schools not matter?
Does having better paid teachers not matter?
Does having the right cultural and social experiences not matter for forming networking relationships?
Does living amongst primarily successful and well educated people offer no advantage offer growing up amongst poor uneducated people?
You are missing the actual realities of trying to educate a poor child versus a rich child. Money grants you educational advantages in hundreds of ways.
You absolutely /can/ buy a better education. Full stop.
The only thing you've mentioned which is a barrier to entry (to elite schools, e.g. Yale) is legacy admission and donations.
The remainder are merely possible causes for non-elite people having lower merit. They are not barriers for a meritorious non-elite person to attend Yale or join the elite.
Does private schooling provide no benefit?
Private tutoring?
Family donations to elite schools?
Legacy admission?
Further:
Does food security provide no benefit to the ability to learn and retain information?
Does a violent environment offer the equivalent value as a non-violent environment, in terms of being able to focus on schoolwork?
Does a multi-parent child receive no additional educational advantage over a single-parent child?
Does having access to paid resources not offer any benefit?
Does attending better funded public schools not matter?
Does having better paid teachers not matter?
Does having the right cultural and social experiences not matter for forming networking relationships?
Does living amongst primarily successful and well educated people offer no advantage offer growing up amongst poor uneducated people?
You are missing the actual realities of trying to educate a poor child versus a rich child. Money grants you educational advantages in hundreds of ways.
You absolutely /can/ buy a better education. Full stop.