What makes you think that one nostr bot posting labeling notes only to it's own relay is centralized claiming of authority? The problem is that nostr:npub1gcxzte5zlkncx26j68ez60fzkvtkm9e0vrwdcvsjakxf9mu9qewqlfnj5z has decided in his app that all report notes should be shown in the global feed and as replies even if they're not somebody you follow or care about. Every other app just uses these if they're relevant to the user. Switch apps, because this IS handled by nostr clients and you're choosing a client which throws it in your face.
To be clear, nostr:npub1gcxzte5zlkncx26j68ez60fzkvtkm9e0vrwdcvsjakxf9mu9qewqlfnj5z is totally within his rights as a nostr client developer to decide how he wants to display reports to his users. Amethyst is open source, he's happy for people to fork it and make versions that work differently, or better yet, provide PR's to change it's functionality.
I think "report" is a terrible name for content labeling because it keeps people thinking that there's somehow some magical secret centralized authority which is getting those reports and taking action on them. That's not how Nostr works. I think we should change the nip to say 'content labeling' and 'flagging users' / 'flagging content' because that's what's happening in Nostr. The apps in the AppStore / Google Play will still need to have it say Report in the UI, but that's their platform monopoly requirements. Relay operators have the power to choose what content they'll host. Almost all do filtering and dropping content based on their own decisions. Nostr isn't a 'you have to listen to me protocol' nor is it a "you have to host my content" protocol. You get the ability to say what you want, but so does everybody else. If you want to make sure your content is online, run a relay. That's what we did with nostr:npub14h23jzlyvumks4rvrz6ktk36dxfyru8qdf679k7q8uvxv0gm0vnsyqe2sh , and we don't put it's content on anybody else's relays at all.
And because it's all open source, you can compile your own version without any content reporting or labeling.