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Inziladun makes a good point in that LotR is from a Hobbit perspective. As far as we know, Sauron might still be a great character in Frodo's time, a charismatic conversationalist with an array of daring and diabolical tricks in the bag, but how can Frodo (the alleged author) know anything about that? That said, I think Sauron well could've made an appearance or two. I would've like to see that. There is after all one character in the book who had met Sauron in person. "He has only four [fingers] on the Black Hand, but they are enough" Gollum says of him.

Before the fall of Numenor Sauron had all his Maiar-traits intact and could still appear as a fair and wise figure. Late in the third age he had long lost this ability for shape-shifting and was no longer able to infiltrate a society to deceive them in person. His physical incarnation was now a tall and terrible Dark Lord with fear and power as his weapons of choice.