It makes sense that games as a storytelling medium would benefit from limited choices. If you leave it completely open, you have no characterization and no plot, because people will make the completely random choice. Even on top of the computing problem, I don't think it's humanly possible to come up with a meaningful story that works for every possible choice. (Especially allowing for how many people respond to games with random/nonsensical choices just to see what happens.)

And yeah, if you've limite the choices to ones that make the story work, make sure every choice you do give people is meaningful.