‘They are all “modern” Gedolim.’
Modern in the sense that they lived after 1800. But all were products of a very traditional Torah education. R’Adler learned with his father and received semicha from Rabbi Abraham Bing. R’Hildesheimer was a talmid of R’Yaakov Ettlinger and R’Yitzchak Bernays. R’Herzog and R’Soloveitchik received most of their early education from their fathers.