The concept of going to a Gadol BiYisroel for a bracha is fairly new.
While Rebbes have been giving brachos for generations, the bracha idea in the litvish world is reflection of the melting pot of Yidden of today’s age. When one went to the Chofetz Chaim, he didn’t just give a bracha, he davened hard for the person, did mitzvos and took on kabalos for the person in need. I don’t recall that any story when someone went to Rav Boruch Ber, Rav Chaim Ozer, Shaagas Aryeh or even the Vilna Gaon for a bracha. They went for eitzas. They went for chizzuk. They went for Torah… but a bracha by itself, comes from the chassidishe world.