DY:
You seem to imply that yeshivos have the advice of a gadol that supports their exclusionary admission policies. I challenge you. Is there any way you could prove that? I have been able to question menahalim and menahalos many times, and there has never been a single instance in which any of the admission policies were set or endorsed by a single gadol. Rather, the attitude is, “This yeshiva is mine, and I will restrict it to whomever I wish. The flavor of my yeshiva is set according to my own personal preferences.” Perhaps such an attitude is legal (or halachically tolerable) but one may justly question whether it fulfills the ratzon Hashem of making Torah education available to all our youth.
Whenever I see a gadol questioned about these exclusionary policies, I always find their responses in the negative. Do you have other experience? The video of Rav Shteinman shlit”a is most expressive, and he is clearly not limiting his response to that specific situation.