An alternative to DNT header might be a "Do Track" header: the browser generates a unique user ID instead of saving server-generated cookies. Users could control which sites receive their ID, manage multiple IDs, or they could reset their ID (like clearing cookies). Sites that still insist on active fingerprinting could be penalized by (opinionated) browsers with scary icons in address bar (like mixed content warnings).
I think there is still value in minimizing passive fingerprinting because it allows servers that don't serve active content (e.g. third-party image servers) to track users.
I think there is still value in minimizing passive fingerprinting because it allows servers that don't serve active content (e.g. third-party image servers) to track users.