Stephen Leacock uses the first-person perspective in his short autobiographical story "My Financial Career," and that is an effective narrative choice in comic fiction.
First of all, telling his story in first person is more interesting. It is generally much more interesting to hear someone tell his own story than to hear him tell someone else's story. Readers would much rather hear him say "I went to the bank the other day" than "Someone I know went to the bank the other day." Even worse is "A guy went into a bank," which is more for spoken (stand-up) comedy than written comedy.
Second, the readers know exactly what the character (in this case, the author) is feeling as he fearfully walks into the bank, armed with years of distrust. While he could try to explain someone else's feelings, Leacock is certainly able to share with us exactly how humiliating this experience was for him.
Third, the first-person point of view adds credibility to the story. This is not just something that happened to somebody at some point in time at a random bank; this happened to him and he knows the particulars and details which both add humor and make the story believable.
Fourth, no one is hurt by his humor except for himself. It is often uncomfortable for readers to hear an author make fun of others; somehow it is more humorous for us to know that the writer is making fun of himself, which gives readers the right to laugh, too.
Finally, the story is told by a narrator, from the perspective of time, who can use humor to teach his readers the lessons he learned. We could not know what someone else might have learned from this banking experience, but we can know what Stephen Leacock learned because it is his story.
Leacock, ironically a former economics professor, once said this about humor:
The world's humor, in its best and greatest sense, is perhaps the highest product of our civilization. Its basis lies in the deeper contrasts offered by life itself: the strange incongruity between our aspiration and our achievement, the eager and fretful anxieties of today that fade into nothingness tomorrow, the burning pain and the sharp sorrow that are softened in the gentle retrospect of time, till as we look back upon the course that has been traversed, we pass in view the panorama of our lives, as people in old age may recall, with mingled tears and smiles, the angry quarrels of their childhood. And here, in its larger aspect, humor is blended with pathos till the two are one, and represent, as they have in every age, the mingled heritage of tears and laughter that is our lot on earth.
Leacock wrote books on the art of humorous writing, and he clearly understood that finding the humor in his life and sharing it was a way for him to cope with the unavoidable (as well as the avoidable) pains and pitfalls he experienced. Being able to see the humor in such things is a gift, and he shares it with his readers in works like "My Financial Career."