There is a problem with the Barnes and Noble analogy. Yes, if you are on mastodon.social and they ban you, you will lose your data. But if you are on hachyderm and mastodon.social blocks you, you don't lose you data (and you can still be seen by the rest of the Fedi). In the analogy, it's like the later case. As long as you trust your server provider your data is fine. It's the same for both network protocols.