Federated ID was a thing for a while. Mozilla ran their Personas service for this exact purpose. OpenID, which is still used for single sign on, was once part of a federated standard. You could use any federated identity provider to sign into any federated website, or you could set up your own.

Almost nobody used the federated part, so all but the most prevalent auth providers (“log in with Facebook”) stayed around.

In theory, you could use the same account for a whole bunch of systems. Mastodon and Matrix both support OAuth2 I believe, so an operator of multiple services (like the Jerryverse) could use SSO to group services and provide accounts under a single login.

There are a few challenges to be solved, though. First of all, if you have a single account, you may expect messages and posts to appear on every single service. That’s just not how ActivityPub is designed to work (it can be, with a smart proxy and some shenanigans, but it’s not going to work reliably). Second, you’ll need support from all services. Kbin and Lemmy have had open feature requests about this for a while, but it’s not high on the priority list. Third, Matrix isn’t interoperable with the ActivityPub platform, so that’s going to need a completely different server setup on the side.

In theory, everyone could implement OpenID and let you log into Mastodon with your Ubuntu One account, but in practice the general public doesn’t really understand how it works.

As for communication, almost every ActivityPub service but Lemmy and Kbin interoperate just fine. That you can’t follow Mastodon accounts on Lemmy is more of a Lemmy shortcoming than a failure of the wider Fediverse.

Matrix just isn’t interoperable with ActivityPub, though I’m sure someone could write a bridge that’ll allow cross service communication. It’s a different protocol built on top of different concepts.