I think it needs to fit your artistic vision. A storygame without any branching would just be a short story (or a novel). It pretty tough to write a short story that can compete with branching interactive storygames, but why not.
There are plenty of story games here that are linear with some premature endings. For example in historical games and certain styles of edutainment games, branching is hard to realize.
Some storygames are built around one central twist. I am thinking for example of Orange's "reelection campaign" to really work, the player has to receive a certain ending on the first playthrough and this limits how much branching there can be.
On the other end of the spectrum there are games that just explore what could happen in a situation and have extreme breadth. Rainbow-1 that you played is an example of that. Here the premise is so brought that a lot of different things can happen and that is part of the fun.