jews have gedolim and gedolai hador. the desire for A gadol hador is foreign to our history. even Rambam or Rabbeinu Tam had others in their generation who contested their position.
the exceptions were few and far between. to expect one gadol hador to follow another is like trying to name the greatest physicist after Einstein died. i think our last acknowledged gadol hador may have been the gaon of Vilna.