Working with a big MS Word document with a group of people using the "track changes" feature is a lot more painful than sharing a software project between a bunch of developers.
Well to be fair that's because you're using it wrong. For the use case you just gave you should be using Sharepoint instead. All that being said, there's other, much better ways of handling this same problem... confluence and google docs just to name a couple.
Just imagine if all the bills that were written were entered into a source control system with hourly commits before they were voted for in Congress. I would be much nicer if people were able to easily see what changed as the bill approached the floor for voting. It would be a lot harder to slip things in at the last moment.
While I love this idea I'll put money down on the table right now betting that if implemented, and all other things being equal, it still won't change the status quo in Washington.