Why a leader would give a speech without telling a story is beyond me.
Stories engage an audience’s emotions, imaginations, and interest. They’re memorable. They communicate important lessons. They make the speaker more personable, more transparent. They’re as fun to tell as they are to listen to. What’s not to be gained by telling a story?
Stories are about conflict (within yourself, with others, with conventional wisdom, with society and its norms, with technology, with nature), the resolution of that conflict, and the wisdom gained in the process.
(As an aside: I believe that audiences are won over more by a leader’s hard-earned wisdom than by any other thing she/he does, is, or says.)
The question, to my mind, isn’t whether you should tell a story. The question is what kind of story you should tell.