Yes. I know, because I am one of them.
First of all, let me point out that vanity publishing is not the same as self-publishing.
Vanity publishing: you have write something for which there is no conceivable market beyond, let’s say, 50-100 copies. No-one is interested in offering you a publishing deal. You pay to have some copies of your book printed, just because you want to and so you have a few copies to give to family and friends.
Self-publishing: you write something for which there may well be a market. You could pursue a deal with a publishing company, but alternatively you could just publish it yourself because it’s a much more sensible option. So you publish it yourself, sell your book via a website, Amazon and through other channels, and make more money than you would have done if you had done a deal for someone else to publish your work.
I don’t know of any vanity publishing authors who are successful.
I know several self-published authors who are successful to varying degrees.
The idea that publishing companies are somehow ‘experts’ in what is or is not likely to sell or be successful is an amusing fiction, unsupported by a single shred of evidence. The only thing they know how to do is follow existing trends (= play safe), publish lots of stuff for undemanding markets (cookery, gardening, celebs, royalty, TV or movie tie-in) and very occasionally take a gamble on something new - a gamble that pays off about 1 time in a 100, if that.
I self-published my own book on cold reading which has become one of the most successful self-published books in history. I’ve sold about 40,000 copies to customers in over 60 different countries. What’s more, it has made enough money for me not to have to work for a living, for 12 years.
The profit I make from each sale of the book is massively more than I would have made if I had done a deal with a publishing company. This was one of a dozen reasons for self-publishing.
I did pay for printing, but I have never paid for any advertising, nor would it make any sense to do so. Also, distribution does not cost anything to me, in that the operational cost is simply passed on to the customer within the unit price of the book.
I have friends who have self-published other non-fiction books that have been very successful, and one or two who have self-published fiction titles.