OK, this isn't a dig at either Heavy Rain (above) or The Birthday Party (below). These interactive videos on YouTube are just a bit of fun. But they do serve to illustrate a problem with interactive movies - to wit, that they are completely and calamitously unengaging.
Look at the Heavy Rain example. It's set up exactly like a scene in a movie. Our mental gears shift to prepare us for being told a story. And then suddenly it all freezes. The engrossing but fragile confection that is story evaporates, to be replaced by the uncomfortable angles of a puzzle. Snap out of it, you have to make a decision!
But as whom? We're not the protagonist. We're not the protagonist's confidant or conscience. We are, in fact, the viewer - or we were a moment ago. But now we're the author - quite a old-fashioned author, too, hopping between viewpoints - making the next plot decision. And in a moment we'll go back to being the viewer. How discombobulating - and exhausting.
Viewers and readers do not want to make up a story. They want to be told a story. The motivation that most compels our interest in fiction is wondering what happens next. Interactivity can play powerfully into this need. You can make the reader the hero, as in a traditional gamebook, in which case their decisions fit logically within the story. Another way is to make the interactivity about the reader's or viewer's relationship with characters.
What doesn't work is disconnecting us from events so that we float around in an oneiric state of immersion one moment, then have to wake up into a different persona - the rational, active self in which we analyse, ponder, sit forward and make a choice. That's interactivity for Vulcans. Let's have no more of it.