Why can’t we have federated identity to login into fediverse instead of creating login for each instance?
Yes, you can. See my post I made on lemmy.world - showing up in the feed of @fediverse@lemmy.world using my mastodon.social account (in the mastodon app). For that to work you have to have the community address and look for it via the search on the mastodon instance.
Screenshot is made in the mastodon instance.