I think the difference is that Cloudflare is the one party providing streaming access for their customers: not just anyone can proxy the data through Cloudflare, they need to be a Cloudflare customer first.

When I'm posting this message to Hacker News, I'm the "customer" of this website. I'm not customer of all the intermediate nodes in the chain. So if I were to write something illegal and HN would be irresponsive to takedown requests, the courts could order the IP of HN to be blocked, not some intermediate ISP.