I'd add: (4) things might change subtly (or not so subtly) as you actually get to doing your game and find that some stuff is not working out well. You may be putting a lot of investment into a design that you'll need to throw away (and you might be reluctant to do so on account of that investment).

An "overall direction" document may be of more benefit. Just 3-4 paragraphs work on each of the major features and how you see it working, and a paragraph or two on the theme/look/feel of each level. Should be enough to ensure that everyone is working from the same basic assumptions but yet give you plenty of room to adjust, refine or discard specific things as the game builds up.