One advantage of using narratives in your speech is that they could explain abstract concepts.
There are some concepts and ideas that may not be easily understood by readers and listeners which is why it details the writer's or speaker's personal thoughts and emotions. Narrating could serve as a vehicle through which the author can describe a personal experience, retell stories or create new worlds by making tales perceived from their own imagination. It is easier to express and convey feelings, views and opinions as these narratives serves as the "true voice" of the author, wherein the words he'll use will be coming from himself.
Another advantage is that you could switch point of views. Narratives are mostly written in first person, using the pronoun "I" to describe the events. However, you can also choose to write it in third person, using "he" or "she" or even second person with "you" to make your speech more expressive and creative.
Also, it gives your writing freedom from research, as you can tell how your mind sees a particular event without having to cite sources or verify facts. If you do choose to research the setting or other particular situations, it adds more weight to the credibility of the speech, which is also a good thing.
You can tell a true story, word-for-word, or if you prefer, you can base your story on an event that really happened and spice it up a bit with contrived events. You can also compile a narrative that is solely born from your imagination.
Storytelling can also be a great persuasive tool. When we hear a story, our brains busily search for a similar experience to relate it to, whether than story is something joyful, painful, disgusting, or anything else emotive. This makes a speech very interesting.
