Yes you could have content specific relays with a restricted set of npubs that can write to them (paid relays basically work like this - when someone pays the fee their npub is whitelisted to be able to write to the relay). Or like you say you could have some sort of restricted web client that writes to that particular relay.

In Damus you can turn relays on or off when viewing the global feed so you get notes from a specific relay or set of relays which would give you a way to view just the content on that relay. I haven’t really looked to see if other clients implement something similar. 

 Didn’t know about toggling feeds on Damus. That’s handy! Particularly when you want a view from a specific relay. Reminds me of ActivityPub where on Mastodon you can follow accounts from PixelFed and Lemmy and those posts will be viewable in your Mastodon client