Ah, except if a relay alters the note after you've signed it, the signature is no longer valid, because your signature is based on the content of the note. If a relay changes the content, then Nostr clients won't display the note, since they only accept notes with valid signatures from the relays.

This is also why it is MASSIVELY important that relays and clients are run by separate entities. If you are reading from a relay that is owned by the same entity that created your Nostr client, they can absolutely alter your note and code their client to ignore the fact that the signature is now invalid.