[[WMG: The spirit of the cauldron was what turned Luna into nightmare moon ]]
It seems that it had great power beyond what it utilized, perhaps it corrupted Luna...
** Keep in mind that these are two non-related universes, with no common points. There is also the temporal issue, in that anything after the film would be using a useless cauldron whose dark magic was nullified while anything before the film began takes place in the film's presented back-story. Additionally, Luna's conversion into Nightmare Moon was perfectly explained in that she wanted to be respected and to achieve this gave into using her powers through her own darkness thinking that as the new ruler she would have the respect heaped upon Celestia. King Sombra might be less-absurd but then you run into the problems of combining the two non-overlapping universes.
*** Not that I don't find this guess to make no sense, but your argument that "after the movie the Cauldron is useless" is debatable. I have seen some fanfics that feature the idea that the HeroicSacrifice ''stops'' the cauldron's effect if they had previously started, but nothing stops another villain from throwing another corpse in it and re-doing the whole thing all over again. After all, why would the Witches have traded the cauldron for anything if it had become totally worthless ?

[[WMG: Eilonwy is not actually a princess in the Disney movie.]]
While she does introduce herself as "Princess Eilonwy", the Horned King actually refers to her as a scullery maid. While you could maybe argue he called her that because he kidnapped her and turned her into one, he calls Taran a pig keeper immediately before that. So it's possible Eilonwy actually ''is'' a scullery maid in the Disney film, possibly working at the palace, explaining her having a nicer-looking dress than, say, Cinderella's attire as a servant, but not princess nice (even compared to Snow White, whose dress is the most similar). Her dress is neat because she's just a palace servant, one that isn't supposed to be mistreated, but she's still just a kitchen maid.
* Actually, calling her a scullery maid was a reference to the book where she worked as a scullery maid. Also, in the book she actually is a princess.

[[WMG: The Sword is powered by the spirit of the Good King]]
Given that the Black Cauldron fuels on the spirit of that dead "evil man", I think we can assume that most magical artifact in the [[TheVerse cauldron-verse]] are powered by the ghost of particular individuals who had a tie with the object when alive. When the sword seems to fight "alone", it's not fighting "alone" per se; the invisible spirit of the Good King is wielding it.

[[WMG: Disney is planning another adaptation of ''The Chronicles of Prydain'']]
The company has been sitting on the film rights to the series since the 1980s, and if they haven't let go of the rights yet after all that time, odds are they aren't going to. ''The Black Cauldron'' has yet to see a Blu-Ray release, when virtually every other animated Disney movie has. Not releasing ''The Black Cauldron'' on Blu-Ray means less people will be able to see it, and connect it to any future adaptations of the series. Enough time has passed so that the demographic who would watch a movie based on ''The Chronicles of Prydain'' will have never seen or heard of ''The Black Cauldron''. It's possible that Disney specifically waited until now when technology has vastly improved, and specifically discontinued the original movie, in order to take another stab at the series with less risk that it would be a financial failure.