"Login with Lightning" with custodial solutions is effectively signing in with the node that wallet uses - user doesn't really own the credentials.

When using Alby Extension, it is recommended to use Master Key (or Nostr keys) to authenticate to Stacker, Geyser, LNMarkets... These keys are yours and we, Alby, (nor Stacker, Geyser, LNMarkets...) do not see them