Hearing recordings of Tennyson read his own poetry or Eliot read his is a bit of a disappointment. The great artist and the great poems aren't matched with a great performance. There are some reasons for this. Tennyson and Eliot were both taught to read poetry for public performance in a style that grates on contemporary U.S. ears. More than that, though, writing great poetry and performing it are two different skills. We assume that they go together. That is our mistake.
There are times and places, however, where the need for those two skills to go together is much stronger than it is here and now. We commonly use a written form of poetry (free-style in Rap and scat in Jazz being notable exceptions) that emphasizes the carefully prepared and polished speech that is to be read, most often silently, by the reader at the time and place of the reader's choosing. However, there is another way of composing poetry, what A.B. Lord calls "composition in performance," and this is the hallmark of oral poetry.
Following his mentor, Milman Parry, Albert Bates Lord became an advocate of the idea that Homer was a performer of oral poetry and that the Homeric texts as we now have them are the result of his collaboration with a scribe taking dictation. Parry and Lord backed this idea by comparing the "diction" and "theme" (or "form" and "content") of the Homeric poems with that of current oral poets in the Balkans. In both cases, there is a heavy reliance on formulaic phrases used to balance out lines and reduce the strain on the performer as he "lays the tracks before the train" composing each poem anew in the act of performance (as opposed to reciting a memorized text of the story word for word). In the case of an oral performer, then, the task is to compose moving poetry while in the act of delivering a notable performance to a live audience. The skills of creating poetry and performing it must go together or the poet fails.
Going back to that sense of disappointment that sometimes comes with hearing modern writers of poetry recite their verse, we have to ask where this idea that skill in composition and skill in performance should go hand in hand originated. The switch from oral to written poetry in Europe and the United States is centuries old. Still, Western poetry is deeply rooted in Homer and oral poetry in general. Perhaps some of this has survived down the ages to manifest itself in that queer feeling that a great writer ought also to be a great speaker.