I disagree, CP is primarily the problem of the site that hosts the media and the site which displays it.

Relays are neither of those, relays just carry text that a client displays. Yes they could carry a URL to CP, but that media is hosted somewhere else and if no client displays the URL, then no CP ever gets distributed.

Trying to moderate at a relay level is even harder and more impractical than it is to do at a client level. Even if you could find a relay admin who wants to actively monitor what makes it to the relay, they would require a client to view that.

I don't think that community-specific relays are a good solution, they go against the idea that relays are interchangeable and will lead to the further fragmentation of Nostr into network islands.

For clarity, I think all relays should have some basic filters in place, but they will always be relatively easy to circumvent. Clients have more options at their disposal to figure out which content to display.