Here's a super-futuristic example, Legend: think of the Star Trek's Holodeck. In the show, there were linear stories one could follow (being an old west hero, for example) that had limited interactivity and specific boundaries, but when the holodeck was made truly customizable -- where the user could make his own setting, people, atmosphere and time period -- all semblance of story evaporated. It was just the person on the holodeck interacting with the things he had created. There was no story except the one he made up for himself.
That's the consequence of freedom: the more you give the user, the less the designer has. The truest form of story telling is where the user has no freedom whatsoever, and the designer has as much as he wants; those are films, books, and so forth. The film maker/novelist can tell whatever story he wants. People may not necessarily like his story, but he can decide every aspect of it.
Interactivity and story telling are directly at odds with one another, and as we increase the amount of interactivity, we decrease the ability to tell a coherent story. Again, just to make sure I'm clear: I'm not saying this is a bad thing at all! I'm very much looking forward to greater interactivity in games, and I definitely prefer more open games, as well. I'm just pointing out that this openness comes at the cost of the developer's ability to tell a story.
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