It depends on the game. I can think of game ideas where linear would not be good. But for the ideas that are whirling around in my head now, imposing some sort of linear structure seems appropriate. What I want to be able to do (given my current ideas) is to give the player as much freedom as possible and still be able to focus on conveying a certain message, theme, etc. I believe that this limiting of action-space can be good for gameplay (as I explained earlier, it does not overwhelm the player), but I also believe it is good for design. The way I have worked on games for over 10 years is to be able to have write down a synopsis and use that in order to plan as much as possible. While I like the idea of the game flowing from some simple start, this is not the way I am used to working and when I have tried it, problems have arisen (it was not until we made proper planning for Amnesia that the project really started shaping up).
I guess it depends a bit on the whole authorship thing too. This is really another discussion, but I can kinda sum it up here: When working on a game there is usually a lot of people involved, even for a small team like us, we have a core team of 5 persons and then the same amount (if not more) of freelancers that handles misc stuff. This means, that once content is made, it is hard to have artistic control and I take on the role as a coordinator more than artist. Sure, there is a lot of tweaking that can be done and tons have been made in projects, but it is mostly on lower level as consistency needs to be kept and there is always fear of the dreaded "domino effect". This means that I would like to be able to "see" the game before it is implemented and to limit the scope of possible interaction it lets me do that. If I would have just let it all flow from a simple base mechanics, it would all be a mess and very hard to keep track of. I guess that sort of development works if you are very few working on the project, but they way we make games now it does not.
I think this is a large reason why many (all???) major game productions feel so "soul-less". Even in games like Bioshock, which has an interesting concept, things are extremely shallow and nobody really wants to take "responsibility" (just check interviews with Kevin Levine where he insists that the game is just about having fun and any message is accidental)
As a final note: I have recently began writing a short story (in Swedish!

) whenever I have time to spare and motivation. There is a vast difference on personality to this work, compared to when I work on game. Even though I pour a lot of myself into a game, I can kind of distance my self from it and not take it so personally. But with a written story, it is very personal and it feels more like a work that I really have to stand for and defend. I would like to have this in a game and to feel that I have really put part of myself into it. Amnesia is a step close, but far from the extent I would like. This does not mean that I need to design everything myself, it just means that I need to be able to "project" myself into at the design process and then make sure it sticks when production starts.
Now this became a really long rant. Sorry bout that