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.
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.