If an AI can generate an infinite number of stories that take place in the LotR world and do it well and faithfully in the style of JRR Tolkien then I would happily read it. You can only read the trilogy and The Hobbit so many times.
You'd happily read it, but that's an answer to a different question. You've already read LotR. An AI generated novel in a similar style doesn't take money from Tolkien's estate.
Some people will want to read the AI generated knockoff. That number of people will usually be much smaller than the number of people who want to read the original and many of those people interested in the AI generated knockoff will also read the original.
The proportion really depends on 1) the quality of what the AI generates, and 2) expectations imposed by the society - in particular, how consumption of AI-generated stuff is perceived as a matter signaling of one's social class. Both are going to evolve rapidly, so it's really hard to tell where we're going to be in 10 years.
With sufficient quality of the model I can certainly imagine people preferring to read AI generated text in the style of Lord of the Rings instead of the original, as the AI generation can adjust the content and style towards the interests of the particular reader, customizing it to deliver what they want.
For example, one obvious observation from looking at fan fiction creations is that 'shipping' is popular, that certain people would strongly prefer certain characters to have romantic relations - and AI generated Lord of the Rings lookalike could have the story with the particular relationships that particular reader would prefer, based on an AI analysis of their earlier reactions to other books; this is not something that we have working today (as far as I know) but we're not that far from it becoming real.
Maybe it's not interesting to see what other people generate with it.
I want to have chatGPT answer my questions, and reference materials when doing that. For example I could paste an article and start asking probing questions, debating it, asking for summary, ELI5, etc.