I'm not sure if they do, but one potential reason not to do it is that setting DNT literally gives the server 1 additional bit of information about your configuration. This could be used to track you more effectively.
1 extra bit is the last of my concerns, there's plenty of bits to uniquely fingerprint a browser anyways. I'd gladly trade one inconsequential bit, which requires malicious intent to misuse, to keep my privacy safe when dealing with honorable entities like, I presume, Google.
Oh, there is so much more that can go into a browser fingerprint. There is no one, single "browser fingerprint." Basically any API your browser exposes can leak information that can be used for fingerprinting. See: https://panopticlick.eff.org/
I don't understand. There are dozens, if not hundreds, or even thousands of bits to use to identify any given browser, but providing one extra such bit that politely asks 'Do Not Track' is now a problem because it makes tracking slightly easier?
https://blog.mozilla.org/internetcitizen/2018/07/26/this-is-...
What goes into one's fingerprint:
1. navigator.userAgent, 2. navigator.language, 3. navigator.doNotTrack, 4. screen.width, 5. screen.height, 6. screen.colorDepth, 7. Intl.DateTimeFormat().resolvedOptions().timeZone, 8. navigator.platform, 9. navigator.hardwareConcurrency, 10. GPU vendor and renderer, 11. isTouch, 12. storage types, 13. font-list, 14. canvas-hash