Many writers became self-published authors for various reasons, and went on to great writing success. Here's a small example. I include only fiction writers under this self-publishing example, as that's our interest here. There have been many, many, successful non-fiction self-published books too.
EL James is probably the best example of self-published authors with her 50 Shades series. She was picked up by a mainstream publisher on the basis of her self-publishing success, and her books have sold in the tens of millions.
Amanda Hocking has also sold millions of her paranormal series of books all under her own steam.
John Locke was the first self-published author to sell over one million e-books on Amazon.com.
Howard Fast self-published Spartacus which, as we all know, became a classic film.
Christopher Paolini self-published Eragon, which was also made into a film although, frankly, hardly a classic. This novel, and its two sequels, was also later published by a mainstream publisher.
Virginia Woolf self-published A Room of One's Own. and other novels too.
Richard Paul Evans self-published The Christmas Box. Again, this was picked up by a mainstream publisher, sold millions and was made into a TV-film.
Beatrix Potter self-published The Adventures of Peter Rabbit
James Joyce self-published Ulysses.
John Grisham self-published A Time To Kill and launched a hugely successful writing career.
Mark Twain self-published Huckelberry Finn, and that led to a rather successful career in writing too.