As long as theres an innate need to externalize our opinions and ideas
the creative process will result. However as technology evolves we might produce art though non-human instigators like mind drafters or dream visualizers so effortlessly that deep thoughts and opinions will become difficult to form and voice over the masses of eventual utilitarian unions of non-artistics that pervade in grand embodiments with their shallow like minded thoughts and art of dogs, cigars and poker tables.
I do not believe artists and musicians will cease to exist in the future. I can't imagine a scenario that would lead to this happening so there's not really much to say about it. Artists and musicians have been a part of human civilization for longer than we probably realize.
Musicians and artist will not cease to exist in the future, I believe that people need music and will always have a need for them. I think as time goes on the music will transform and become new and different things we never considered but we will still use them.
Humans will always have the need to be artistic and musical, even far into the future. Art and music even have mathematical foundations, so if humans ever become cybernetic organisms hooked directly into computers, those facets of humanity will always be there. Art and music have been around since the dawn of mankind and will remain there for many more millennia.
Art and music is humanity - its implicit, and will be around for the entirety of human history. Art and music will only proliferate and become more diverse as computers and cheap physical supplies make creating and enjoying both far more accessible to average people, instead of just those who can afford it.
For as long as humans have been around, there has been art. Human life and art coincide with each other. They have a symbiotic relationship. Humans have always created art, and will always continue to make art. I do not think that artists or musicians will cease to exist in the future.