It would be a conspiracy theory to say they were created by a three letter government agency, but if I was running one of those three letter agencies, this is exactly the kind of company I'd setup and control. People just give them their TLS keys lol
If you use a VPN or just like browsing in privacy mode, it will make your life as difficult as possible by having you fill out multiple captchas. And even then, it will sometimes not let you through.
If you're running a website, please stop using Cloudflare.
I use VPN and private browsing and the worst I've been subjected to is getting IP/ASN blocked, which to be fair can be implemented without cloudflare. I've had to fill out captchas but that's something that happens a few times a month at most, and it's never a captcha loop that you mentioned.