Without the incentive of being able to profit from their creativity, many creative industries could potentially suffer from a significant decline in the production of new content (including film, book publishing, visual arts, video games, software/applications and more). Individuals may still create artistic works out of personal interests or because of genuine joy and passion of creation alone - however, a career dedicated and specialized entirely to creative output likely cannot be sustainable and feasible for a majority of artists without any financial rewards attached.
Ultimately, it is difficult to predict exactly how the music industry would look without copyright laws. Still, it is safe to say that it would be very different, potentially less competitive with fewer economic incentives or rewards for creating original materials that could easily/quickly be replicated at scale.