> they select for students that had the luck (or the right parentage) to go to either a private school or to a public school in a well-funded school district.

They select for math ability, it just so happens that students with access to great resources get better at math than those without them.

> The result is that the student base will be overwhelmingly white rich kids, which is pretty problematic Pretty clearly not true. It is overwhelmingly asian kids and while wealth plays a factor, poor asians still do exceptionally well (IIRC poor asians do better than rich whites). This can never be acknowledged because it makes people less sympathetic to your point.

> purpose of academia - that is, to provide education and research opportunities to the actually gifted instead

A students innate ability is irrelevant for college admissions. What matters is what are your actual capabilities. Are you capable doing mathematics at the highest level or are you not? An innately talented student who is bad at math due to life circumstances out of their control is still bad at math.