I've been thinking for a while that the web really suffers from not having a built-in concept of (ideally fairly anonymous) identity. I shouldn't need to maintain a whole authentication system and a database full of PII just to let you see the same data across your laptop and your phone...
The browser should be able to vend me an (opaque, anonymous) token that identifies you as an individual. If your mobile and desktop browser vend the same token, then the website sees you as having the same identity on both platforms.
And it's a poor enough solution that we have to build extra layers around it (for example, Apple's auth "login with Apple ID", which lets you hide your real email address behind an anonymous relay)