This has been mentioned before around here, but I think the obsession with "story" is a more recent thing. I know there's one top Imagineer who's always going on about it.
In the strictest sense, a linear story is not as cool as a more generic experience, in part for the reasons mentioned above.
Take the Mexico ride, for example. The old attraction had some weaknesses, but it seems an altogether more pleasurable experience than the "story" of "Where's Donald?". Well, there he is. Story over.
The older version felt more like exploration than being led by the nose, and in my young imagination, it felt like there was simply more to it.
I always imagined there was much more to Pirates, just around the corner, even though I know I'd probably just find some plywood, hydraulics, or maybe an emergency exit.
For dark rides, I tend to prefer an open-ended experience like the original Journey into Imagination. Even Horizons, which had narration, didn't have a strict storyline. It bounced around, showing you the wonders of tech and how they'd affect lifestyles, but it wasn't the same as following a single protagonist around.
When you're exploring, there's always more to see, but when you focus on story, then once you know the ending, something is lost.
You can even make the comparison between something like Captain EO, which told an explicit movie-like story, to Magic Journeys, which was just a headtrip. Journeys seemed a much better fit to me, in the Imagination pavilion.
If you'll forgive another metaphor, it's the difference between moving through an open-ended video game, finding little Easter eggs and tricks you can do, as opposed to being led around on a rail, punctuated with cut scenes you can't interact with.
I'm not sure this holds true for all attractions, however. And people do watch their favorite movies over and over, and the best of them provide new discoveries each time through. Some things do just work better as stories, but I think the most of the exploratory attractions do more to stimulate the imagination.