It's a very good question, and I would certainly grant that writing in dialect can serve as a barrier to entry. That being said, I think this technique is used very effectively within this story, and that the story itself would not work quite as well without it.
First of all, writing in dialect adds an element of authenticity to the story. "The Celebrated Jumping Frog of Calveras County" is ultimately a depiction of everyday life, and trying to encapsulate everyday patterns of speech is a highly effective tool in the realist's repertoire.
Additionally, Twain's story here is shaped by a very powerful contrast between the erudite narrator, who speaks in very precise and very proper...
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