That nobody respects is is a false statement. Some do. Also that header permits users to signal sites if they want or not to be tracked, avoiding cookie popups.
Edit: I just saw that Firefox supports GPC, which seems a better alternative to DNT.
But others use it as a signal. You are easier to track by the dishonerable with it. Meanwhile the honerable were probably not tracking as much [no way to tell but a reasonable guess]
You might be easier to track with it, but it is not hard to end up with a unique signature anyway. I can already be uniquely identified, so sending "Do Not Track" only has potential upsides. I have seen websites that claim to honor it so it seems to be doing something and I wish they wouldn't remove it.
I looked into GPC, and I'm not sure if it's much better. From the implementation notes[0]:
GPC is also not intended to limit a first party’s use of personal information within the first-party context (such as a publisher targeting ads to a user on its website based on that user’s previous activity on that same site).
GPC also appears to use the same tracking signals as DNT, so it has the exact same potential for abuse, as far as I can tell. Maybe I'm missing something, but unless there's legal power behind this, I'm not sure if it's better.
Edit: I just saw that Firefox supports GPC, which seems a better alternative to DNT.