the ability of a student to strategize is strongly correlated to the education and wealth of the parents. (as pointed out in the post).

the discrepancy in strategic aptitude is itself a result of chance. Only through this absolute form of randomness, you are actually eliminating the wealth, education and aptitude bonus of upper-class households.

Your comment is a nice signifier of the difference in American and Dutch culture. Dutch people don't buy the idea that individual strategizing is going to advantage the interests of lower-class students, because they recognise that lower class students are already disadvantaged when they enter the system.

Generally speaking, we're not trying to reduce random factors. We're trying to reduce hereditary factors. There are already plenty of intrinsic hereditary factors (intelligence, appearance, health). We want to limit the ability of extrinsic hereditary factors (wealth, connections) to influence egalitarian processes, and in some cases even correct for them.

The particular skills considered necessary to succeed in a meritocratic society tend to get defined post hoc.

Its much more likely to be a result of a "parental wealth gap", because its those who are going to pay consultants lots of money (and likely conspire with other wealthy people to rig the system) to ensure optimal placement.