Not really. Most relays used by our user are not supposed to be shared with anyone anyways... Who cares which relays you are downloading your posts from, how many feeds you have and so on... That should be all just for you. On Amethyst, those are all private lists.

The ones on the outbox kind were made just for the followers, not for the user himself. There is no place for the user's own relays in that kind.