I think this has a lot to do with the nature of the ring. As the story progresses and Frodo becomes more and more under the influence of the ring, he can no longer be the "everyman" character. That role, by necessity, has to fall to Sam. I suppose Tolkien could've tried to write the story from Frodo's point of view as the ring begins to take control, but then it would be a very different story and a very different narrative experience.
"In the next day or two Frodo went through his papers and his writings with Sam, and he handed over his keys. There was a big book with plain red leather covers; its tall pages were now almost filled. At the beginning there were many leaves covered with Bilbo's thin wandering hand; but most of it was written in Frodo's firm flowing script. It was divided into chapters, but Chapter 80 was unfinished, and after that were some blank leaves. The title page had many titles on it, crossed out one after another....
'Why, you have nearly finished it, Mr. Frodo!' Sam exclaimed. 'Well, you have kept at it, I must say.'
'I have quite finished, Sam,' said Frodo. 'The last pages are for you.'"
So it should be no surprise that Sam takes more prominence near the end of the story... he may have been the one writing those parts, or at least editing them!
The parallel between Frodo and Sam, and JRRT and his son Christopher, strikes me as somewhat interesting... I wonder if JRRT knew he would never finish his "history" of Middle Earth?