By “claiming addresses” you mean domains? Or what?
You mean because the address in the fediverse scheme would be domain-independent? How in the world would that work? How would it know what to connect to? You’re proposing something completely different than ActivityPub at least.
Okay, sure you could have apps open links to external posts, as the app would know that it would need to fetch the post by searching the URL (switched with a HTTPS scheme). I can kinda see the point of that. I’m not sure the fediverse and ActivityPub is really super mature enough for that yet. For instance you can’t fetch Mastodon posts from Lemmy.