If I route an illegal stream via something like Cloudflare or Cloudfront, will the court ask the ISPs to block all cloudflare IPs? That's not going to go well.

I guess Cloudflare could block the stream, hopefully in time for that to not happen, but it seems risky.

If the stream uses something like https://webtorrent.io/, your going to have to block the IP of everyone else in the world watching it.