A report content form, like DMCA, with support people behind processing the tickets. It already exists.

When there is phishing or pedo content, you think they wait for court order or react to abuse ?

They are distributing content through their servers, not just displaying it.

Every hosting and CDN companies has abuse department, it's a normal part of the process. Here, Cloudflare is aware, and chooses to ignore the abuse requests, then they have to take their responsibilities.

Cloudflare is a US-based company so they are realistically out of reach, or too late.

If there are abuse requests, and Cloudflare wants to comply but not block the website, they can downgrade to DNS only, and then the host IP would be blocked.

If Cloudflare doesn't comply and intentionally keeps distributing content -> block Cloudflare.

At some point for them, the cost of complying with the law will be cheaper than handling the complaints that they are blocked.

It's like YouTube, they shutdown content on request of rights holders.

Afaik, Cloudflare are asked to block an IP, to which they answer that is not a valid IP, but a shared one, please be more precise. Being more precise takes effort and time, so they opted to ban the IP at ISP level, and they don't have to ask anyone.