Just imagine a movie, where 3D is not used as a distraction, but in harmony with the movie; and where the story is complex and beautiful.
The only question is, which movie will it be.
The only question is, which movie will it be.
Not which movie, but how to create such a movie. How would 3D effects harmonize with a movie? How would 3D add to the "complex and beautiful" story?
After solving how, we can answer "which".
That said, I do think detective stories or other slow-pace movies could genuinely benefit from 3D. The first few would be hopelessly distracting, but eventually people might come to accept the concept, and then you'd be near equal ground with the protagonist. A room full of distractions, some of which the characters draw your attention to; A man on his deathbed, occupying only a corner of the bed and unable to reach the water clearly under a meter away; A couple wandering the streets at night, afraid of thugs until they dodge into a warm and sheltering tavern. I think these kinds of movies could genuinely benefit from a more immersive environment ...eventually.
edit: more likely, by the time people can make such movies, the technology will be commonplace enough that no one will notice, except maybe to complain about how they didn't take proper advantage of it.
The solution to all three questions is exactly what's happening: throw as many parallel filmmakers at the problem as we can spare and wait to get the answers. (Of course, the question "can it be done" is undecidable.)
The thing is, conventional 2D movies already have most of the 3D cues we need - blurring, parallax, etc.
Adding these elements would be far too distracting. And if we weren't distracted by sound and color, then what's the point in having them there?
Artists should work in the most limiting possible way -- in a way that everyone is already accustomed to. Otherwise, they're cheap, tawdry sensationalists. Down with change! Down with innovation!
Wait... what?
NO COLOR vs COLOR isn't the same as "n 3D cues" vs "n+1 3D cues".
A better analogy would be
"All colors apart from a particular shade of purple" vs "all colors".
Of course the current systems are rubbish, so you're getting an extra 3D visual cue at the expense of clarity sharpness brightness. And headaches thrown in to boot.
Think about Technicolor, for instance. Unrealistic, and to some, headache-inducing. But it was an early step toward what we have today.
These days, most films are shot in color, and in a fairly naturalistic way that people don't generally notice. But that certainly doesn't mean there's "no point in having it there." It's just a greater level of immersion, which helps draw people even further into what actually matters (for most films): the story, the characters, etc.
And "How to Train your Dragon"?
The only movie I've ever seen where 3D added something to the experience was an IMAX documentary about fish played in a ten-storey high screen. Combine the three-dimensionality with the peripheral-view-filling nature of the IMAX screen and you really have something. I think it might work better for documentaries than for narratives, though.