We don't need a header to specify that the user wants the default site behavior. It only makes sense to send any header at all if the browser actually has some information that the server doesn't have (whether that's user preference or browser capabilities). Sites will continue to do what they're presently doing for users who don't do anything explicitly. They'll only change their behavior for users who do something explicitly, which means that, in order for this header to be worthwhile, it must be possible for users to make the setting more restrictive than the default. Changing the default site behavior is a legitimate goal, but it's not a technical goal that can be accomplished with a protocol extension. The value of a protocol extension is to let requests be different from each other, so that sites can treat them in different ways and comply with actual desires.
If you want sites to pay any attention to any new header, it must be in the site's interest to do so; otherwise, they'll ignore it in ways that are just hard to notice. In order to get sites to actually respond to the DNT header, you need a substantial portion of the people who set it to 1 to watch for site being inappropriately knowledgeable and avoid them and tell their friends the site is creepy. If the general population isn't going to contribute to enforcement like that, it'll be meaningless if it's the default.