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.
This is convenience and privacy, with a SolidPod you decide who stores the data. It could be you, it could be any federated instance, but that data is encrypted and you decide which application can use which data. They use a WebID (see this as a hash of your unique profile) to identify the user and this would be the only data that is shared between you and any federated instance.