Technically you are correct but look at the demographics of who applies because of the expense.
Even need blind schools are loaded with the wealthy.
Some kids don’t apply due to the cost.at Brown, as one example, over half are full pay.
Having money gives you a confidence to even apply whereas many who are not of that livelihood don’t even truly have the resources (non financial) to even consider these types.
That’s why I note it as a hook but technically you are correct.