This analogy seems to be made every time this comes up on HN, but I don't think it really holds water. First of all, when a human artist learns from another, it's inherently a level playing field for competition; the junior and senior are both human, neither are going to be 1,000,000x more productive as the other. So the senior artist really doesn't have that much to worry about. And the senior artist recognizes that they themselves were once a junior and had to learn from their seniors, so it's a debt paid forward which results in more art. And becoming a master artist or even an imitator takes dedication and hard work, even with lots of artwork to learn from, so that keeps competition to a certain level.
When it takes decades to develop an art style that a machine can copy in days, and then churn out derivative variations in seconds, it's no longer a level playing field. The machine can dramatically under-cut the artist who developed their style, much more than a copycat human artist could. This does become not just a threat to the livelihoods of artists, but also a disincentive to the development of new art styles.
In this case, patent law may be an apt comparison for the world we're entering. Patent law was developed with the idea in mind that it is a problem if a human competitor could simply take an invention, learn how it works, and then mass produce copies of it. There are several reasons for this, including creating an incentive for technology development, and also expediently transitioning IP to the public domain. But patents were added to the legal system basically because otherwise an inventor would not be on a level playing field with the competition, because it takes so many more resources to develop a new invention than to produce clones.
Existing IP law was built in a world where it was believed that machines were inherently incapable of learning and mass-producing new artistic works using styles learned from artists. It was not necessary to protect artists from junior artists learning how to work in their style, as long as it wasn't a forgery. But in a world of machine learning, perhaps we will decide it's reasonable to protect artists from machine copycats, just like we decided it was reasonable protect technology inventors from human copycats.
The patent system is not the right implementation; it's expensive to file a patent, and you need skilled lawyers to determine novelty, infringement, and so on. But for art and machine learning, it might be much simpler: a mandatory compensation for artists' work used as training data. Something like this is sometimes used in the music industry to determine royalties for radio broadcasting, or to account for copies spread by file sharing.