Honestly for a platformer a complicated story just brings it down most of the time and simple is usually better.
It doesn't have to be complicated (or as Blue Valkyrie said, convoluted). But I would appreciate something that was a little
original, something that would interest me beyond just the gameplay.
I should also add that the trailer explaining the story was also not a good idea. As Other M has shown me, you can't expect a story to work if it relies solely on exposition. There needs to be interaction, emotion, subtlety, etc. There was no need to give us what is most likely the website plot summary of the first 20~40% of the game.
Honestly I think more gaming companies could stand to do what Inafune and Nintendo Direct are doing, because otherwise I barely know the people behind the game besides their names.
I agree with that, but I really don't think Inafune is heavily involved with this game.
Personally, I don't even see Inafune being heavily involved in the creative process, he mainly is just quality assurance by giving feedback. Hideki Kamiya stated that he's a businessman more than he is a creator, and I see a large degree of truth in that.