I don't understand the benefits.

users don’t have to scratch their head on if I am the same person or not across these platforms

They already don't need to worry about that. Presumably if you could log in with your Lemmy user on Mastodon, your user domain would still refer to your Lemmy instance, just as it does currently. That's besides the fact that I have no idea how this mechanism of logging into different sites would even work.

theoretically, someone following my feed can get updates on what I do on multiple platforms

They can already do that with the current mechanism. It's only a problem with Lemmy not supporting various other forms of social media concepts that prevents you from writing, say, a toot (microblog).

It sounds like what you want is just a more generic ActivityPub instance that supports more forms of social constructs.

Aside from all that, there's what other people have mentioned. Grouping users on instances has all kinds of moderation benefits.