If you don't do this, the third-party cookie blocking that strict Enhanced Tracking Protection enables will completely destroy your ability to access websites hosted behind CloudFlare, because it is impossible for CloudFlare to know that you have solved the CAPTCHA.
This is what causes the infinite CAPTCHA loops. It doesn't matter how many of them you solve, Firefox won't let CloudFlare make a note that you have solved it, and then when it reloads the page you obviously must have just tried to load the page again without solving it.
You realize this is the same as session cookies, which are used on nearly every site, even those where you're not logging in?
>This sounds like "we only save hashed minutiae of your biometrics"
A randomly generated identifier is nowhere close to "hashed minutiae of your biometrics".