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.
This sounds like "we only save hashed minutiae of your biometrics"
Yes?
HTTP is stateless. It always has been and it always will be. If you want to pass state between page visits (like "I am logged in to account ..." or "My shopping cart contains ..." or "I solved a CAPTCHA at ..."), you need to be given, and return back to the server on subsequent requests, cookies that encapsulate that information, or encapsulate a reference to an identifier that the server can associate with that information.
This is nothing new. Like gruez said in a sibling comment; this is what session cookies do. Almost every website you ever visit will be giving you some form of session cookie.
What is not within your rights is to require the site owner to build their own solution to your specs to solve those problems or to require the site owner to just live with those problems because you want to view the content.
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".
Your assumption is that anyone at cloudflare cares. But guess what, it's a self fulfilling prophecy of a bot being blocked, because not a single process in the UX/UI allows any real user to complain about it, and therefore all blocked humans must also be bots.
Just pointing out the flaw of bot blocking in general, because you seem to be absolutely unaware of it. Success rate of bot blocking is always 100%, and never less, because that would imply actually realizing that your tech does nothing, really.
Statistically, the ones really using bots can bypass it easily.
Tor and VPNs arguably have the same issue. I use both and haven't experienced "infinite loops" with either. The same can't be said of google, reddit, or many other sites using other security providers. Those either have outright bans, or show captchas that require far more effort to solve than clicking a checkbox.