We use AUTH on many of our relays for different reasons.

nostr.wine - AUTH only for kind 4 REQs to protect DM metadata

filter.nostr.wine - paid proxy relay service, AUTH on connect for access control

creatr.nostr.wine - patreon relay with granular event access control, AUTH on connect

inbox.nostr.wine - special purpose access control relay for DMs, giftwraps, and NWC events. AUTH on any REQ. Events can be sent without AUTH as long as the tagged pubkey has a registered inbox.