Limiting interactivity is not what we're supposed to be about here. A few games have actually done this, but they were universally acknowledged to be bad games - certainly not the ideal example of interactive storytelling. If the player's not ready for the dramatic climax, that's tough. In this case, you can create a world that's alive, that goes on around the player, regardless of what he's doing. This makes for some really interesting adventure games.
Night falls, and people come out of their shops and go home, and the muggers come out, and so on.
It's interesting to watch things take place around you in one of these kinds of games. The difficulty with them is that you tend to lose the game a lot. You end up having to start over all the time, because you weren't ready for the dramatic climax when it occurred. It would drive you crazy. But saving the game utterly destroys my suspension of disbelief.