Here is a story proving my point from the excellent book “In Their Shadow”, Yonasan Rosenblum’s English translation of “???????” by Rabbi Shlomo Lorincz, which is chock full of selected stories about The Chazon Ish, the Brisker Rav, and Rav Shach. I highly recommend it for anyone who’s looking for an honest look at what made these 3 Gedolim. On page 16, the author is discussing the fact that many yeshivas of his time refused to take Sephardi kids. One such Rosh Yeshiva told the Chazon Ish that he didn’t take Sephardi kids because he felt they would not be successful in their learning. The Chazon Ish said back, “If that’s the case, how is it that you study the Rif and the Rambam?” In another story, a Rosh Yeshivas rejected Sephardi kids because they don’t speak yiddish, the teaching langage of the school. The Chazon Ish advised the man to switch to ivrit so he could accept Sephardi kids. Keeping the language as Yiddish would force kids who don’t know Yiddish to worse schools, and the loss would outweigh the gain of not speaking ivrit.
Today in Israel, the shanda of segregating Sephardi and American kids is a reality, despite our Gedolim.