There would be no incentive to write great literature if this were the case
I think you misunderstand what it means to be a writer. Rainer Maria Rilke: "Find out the reason that commands you to write...confess to yourself you would have to die if you were forbidden to write." Authors ought write because it is something they love to do, because they want their words and ideas spread to others. The world would be a better place if authors were motivated purely by their love of writing--because "you would have to die if you were forbidden to write"--rather than incentivized by fame.
I believe that if someone wants to put their name on their work and receive due credit for it, they should be allowed to. Behind every work of art, their is an artist, and I believe that it is the artist's right to receive due praise.