That is indeed their goal - this kind of
targeted harassment is done deliberately to collect more personal data of the user.
This tactic is quite common among BigTech and something I've experienced with both Google and Amazon - once you are hooked onto their product, one day they will suddenly deny some aspect of their service to you and force you to share more personal data with them to get access to it. For example, Amazon will one day start to ask you to click a link sent to your mobile to access their account, or Google or Microsoft will block your account and ask you for your mobile number to "verify" you etc. When you are blocked from using a service suddenly, however privacy conscious you are, in your desperation you will be forced to comply.
I have experienced this with CloudFlare too once when many website were suddenly blocked for me by CloudFlare on all browsers and I was forced to install their extension to access some information I needed from a website urgently. I have no doubt in my mind that even otherwise, they just deliberately and randomly blocked access to some sites and displayed their "captcha" page just for PR and "brand awareness". Now that CloudFlare has realised this is backfiring on them because of the negative emotions being associated with their brand, they have now redesigned their "captcha harassment" page to give less prominence to their branding than before.