True, they live in your head rent free. But if you produce a derivative work, you have to pay.
A trivia host doesn't have to pay royalties to ask questions, and the players don't have to pay royalties to answer them. If that turns into "movie night" at the bar then they have to pay royalties to screen the full film. If a professor plays clips in film class, he doesn't.
Your implication is that an LLM is little more than an brilliant film scholar or exceptionally well-read librarian, and that the matter is settled. The billions of dollars in play across a dozen active court cases say it isn't.