I'd argue that people do care about Gollum, but in his role as a weird creature twisted by the ring. A sort of horror cautionary tale. That doesn't mean he can carry a story as the protagonist. Some stories don't need to be told, some might be more effective if you leave some of the mystery even.
That said I don't think there's any story idea that's impossible to mine something from; if someone has a really interesting idea about Gollum they need to share in movie form who knows? If an exec was like "Hey make me another one of them lotr films, they make a lot of dough, I don't care about what, how bout that Gollum guy" it's probably doomed to suck tho.
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