If people would host "abc liked my tweet" and "xyz follows me" on their own server, then everybody would claim that Billie Eilish liked all their tweets and Joe Biden is their best friend.

People go on social media for the social graph.

You can do that via a central authority (and live in fear that everything is taken from you) or you can do it via cryptographic proof. Self hosting is not a solution.

You also cannot host identity.

If your domain gets stolen from you (search for the horror stories on Google or HN search), your identity is gone. Nothing you can do against it, since you are at the mercy of authorities again: The registrars.