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I guess you feel very authoritative in speaking for every student in every school in every situation with making this very dogmatic statement. There is at least one active commentator here whose child did self-study Calc, used that advancement to engage CS / Engineering research and ultimately attended MIT. So to the question of whether self-study of anything can help - in your words “no it won’t”.
I would disagree with you that the multifactorial admissions process and its uncertain outcomes should lead to nihilism (apparently according to you on every front) - Nothing matters because nothing is a guarantee.
If students don’t lean into squash, get a job or start nonprofits with any eye that it will help with brand name admissions, well there are a lot of coaches, companies and groups that should be out of a job. I guess we shouldn’t strive for anything right? You’ll get what you get and not get upset!