That genericism is certainly a contributing factor; D&D is a system, not a story. And I think you're right, that folks developing screenplays are probably telling the most darling little tales from their game tables, which, you know, may not even be appealing to much of the core fanbase. Vis, the first movie.
I'm not a fan of the FR or MtG settings. But these at least have a presence and fans way from rulebooks. To have how many video games and a perennially popular CCG and novels, and not be able to mine them for decent stories a wider audience will appreciate? Oof. I do see that turning toys into shows/movies would be easier than adapting a rulebook, but... Come on, man.