Unlike real art, computers can produce a trillion unique works an hour. This will apply to all forms of art in the future, including stories, music and movies. So where is the scarcity?
I'll also add that scarcity will be simply built-in. Most folks won't initiate such art - and such art has to be initiated. There will still be a personal selection process going on with a human behind the scenes. Just because the computer can make so many doesn't mean we'll see that many at all. I imagine it will eventually edge out some art forms: Making advertising graphics for movies and print, for example. Making logos. And so on.
Up one meta-level. The artwork isn't the sonata, or the portrait, or the sculpture. The artwork is the algorithm and input data.
It's the same logic with e.g. books: if there are 100 great books, people are going to love those books and some subset of people are going to find a book and say, "wow, this book was really meant for me". If there are 1,000,000 great books, then 1) there's going to be a wider selection for people who enjoy more niche aspects in books who wouldn't otherwise find those, and 2) there's a much higher chance of one of those million books really resonating with any random individual.
The real struggle is in curation and recommendation: which of these million books would John Smith _most_ like (ideally more than, say, the original 100 books), instead of requiring him to peruse through them all on his own.