The vast majority of AI image prompts don't reference an artist name, and the ones that do are typically using it as a proxy for a given style and would generally get similar results by specifying the name of the style instead of the name of the artist.
The ones using the name of the artist/studio (e.g. Ghiblification) also seem more common than they are because they're the ones that garner negative attention. Then the media attention a) causes people perceive it as being more common than it is and b) causes people do it more for a short period of time, making it temporarily more common even though the long-term economic relevance is still negligible.
The latter example (Ghibli) is also somewhat misleading. Other studios sometimes use very similar styles. They might not have the same budget for fine detail throughout the entire length of the animation, and they probably don't do every production with that single art style, but when comparing still frames (which is what these tools generate after all) the style isn't really unique to a single studio.
The ones using the name of the artist/studio (e.g. Ghiblification) also seem more common than they are because they're the ones that garner negative attention. Then the media attention a) causes people perceive it as being more common than it is and b) causes people do it more for a short period of time, making it temporarily more common even though the long-term economic relevance is still negligible.