Cloudflare is just another corporation with greed in their eyes and if you don't design yourself to their puzzle than you're not welcomed.
This is an extra wall in walled garden land; another one you will need to jump if you want to break free. Another stab at gatekeeping the upcoming Ai era of the internet. It's no different to the playbook of Google, Apple, and Facebook of the 00's. So, no, you're not paranoid.
In the terms of security: My firefox on FreeBSD instantly triggers endless loops of "prove your human" on their turnstile. I can't use old handhelds of android and a single VPN triggers all. Anything that they don't see as "secure" you're denied from.
What is stopping Cloudflare from deeming your LLM as unsafe?
Scenario: You're ready to launch, you come up with the next best innovation for the next generation of Ai internet. Revolutionary and you're about to launch, blast off; wait. You're denied your launch because it threatens their service. The former: they like your idea more-so and clone it to become theirs.
Stories of above have all been posted on HN before. Startups have been sabotaged by rug-pulling of cloud providers. It is early-vendor lock-in and at it's best. Google & Co would be jealous; if they were not in bed with.
This will turn in to a netting of: Your Ai isn't using our service, so your Ai isn't allowed to interact with ours.
What does Cloudflare offer as a service? A turnstile to the Internet of Things and the difference this time is that you get to self-host your own corner on their patch of land with their ticket prices and access policy of.
Remember folks, no corporation gives a rat's ass about you. Internally, or externally, you're just another sheep to extract wool from.