This somehow assumes that your fingerprint is going to vary, and be unique, every time you interact with a tracker. That’s basically not ever going to be the case for casual use.

If Cloudflare fails the tick-box Captcha and I need to tell it what squares contain motorcycles, that would suggest that I currently have a unique fingerprint that they do not have yet enough history on to tie to a person. How often do you get to do the square puzzle nowadays?