DaMoshe: It has nothing to do with the Scots or Scotsmen. Theoretically, perhaps, YU could have produced a godol; if not for its krum hashkafas that are kneged HaTorah. But given that YU is what it is, it had about as much chance of producing a godol as the Princeton Theological Seminary has.
Square: Rav Pinchas Scheinberg zt’l was a talmid in Mir (in Poland) and in Kaminetz (also in Poland, at the time.) That’s how he became a godol. Not because went to NYC public school and YU (both of which he passed through).