Depends if you mean a read-restricted relay you run or one that you don't. In both cases though, it's different because anyone with access to this read-restricted relay can copy the notes, and those notes are cryptographically linked to you, and depending on who you are you might not want that. (And in various other ways too.) You might want the cryptographic link to be between you and your space, as opposed to between you and your notes.

if you want that you can just have a relay that signs notes with random keys anyone reading from that will know they are from you, but the signatures will not mean anything