I actually don't think it'll be a problem. Art, even with AI, will be appreciated. The actual problem is going to be keeping artists motivated to continue their craft. I mean, the second someone spends nine hours painting a rose, and then, they ask AI for a little assistance, and poof, in 2 seconds it produces roses better and more flavorful than the painter could, they'll eventually stop. Same thing with writers. The second someone writes five chapters in a book they have poured the soul into, and then bam, five seconds later AI creates the next 12 chapters - and they are better or just as good. There will be a point when the artist just shakes their head.
I imagine two things: The artist that refuses to use technology to help them, insist they are there for the art (the heartbreak and joys), and then create only to have AI generate hundreds of thousands similar. The joy, unless it is to give to grandkids or friends as a Christmas gift, will slowly fade.
The other thing I imagine is definitely going to be common. The artist that "looks" like an artist, talks like an artist, and is applauded as an "artist." Then we will find out their song, their book, their photo, their, whatever, was AI. That, sadly, will probably happen so much, that in the end, people will start to disassociate the artist from the art. The artist will become a salesperson. An actor. And no one will care.