Jorge Luis Borges wrote a story called "The Quixote of Pierre Menard", about a man who rewrites Don Quixote word-for-word. But because he writes it from a modern perspective, it has a different meaning, and is a different work of art. :)

It seems unreasonable to me to suppose that there aren't already people writing Beethoven-style symphonies as well as Beethoven did. We probably have many times as many composers as talented and as well-trained as Beethoven was. Composers today have recorded music, easy access to scores, synthesizers, all sorts of advantages. And they've heard Beethoven. They should be better than Beethoven. My guess is nobody pays any attention to them.

(And if somebody wrote plays today in the style of Shakespeare, and they were as good as Shakespeare's, I don't think anyone would publish them. Publishers would laugh at the artificial, overly-stylized language, the monologues, the poetic form, the coincidences, the crude sexual puns. Everything people love about Shakespeare is considered bad writing today.)