In response to Bray’s toot, Evan Prodromou — one of the creators of ActivityPub, who is currently writing an O’Reilly book about the protocol — noted that this “is also the argument for using the ActivityPub API.” He described the API as “an open, extensible API that can handle any kind of activity type — not just short text.”
This gets to the nub of the issue. The fact that I can’t use my Mastodon identity to, for example, sign up to Pixelfed is not actually an ActivityPub issue — it’s because the two applications, Mastodon and Pixelfed, each require you to create an account on their respective products. What Prodromou is suggesting is that, technically, you can use the ActivityPub API for account access.
Creating different accounts is the only way to have privacy in the first place. Different logins makes you look like you are different people. Which is the point.