"Why would I write a game design document for a tabletop game"?

Answer: you don't. I have never heard of it being done. Sometimes, when you're ready to approach a publisher, you'll write a description for the potential publisher, but this is nothing like a game design document, as it is a marketing tool. If the publisher is sufficiently interested in the game they'll try it out, why would they need a document that describes it when the game exists to play?

When you think you know what you want in your game, make a prototype. If you don't know what to do in the prototype, you haven't thought about it enough. Even after you make the prototype, you'll change it a great deal as you playtest it. So why write a design document?