I wouldn’t say censorship alone is the primary motivation here so I’m a bit wary when people bring it up. But the way to think about it is that your data being on PDS is the mechanism that creates a market opportunity for other apps that, among other things, differ in moderation strategies.
Concrete example: Bluesky banned a person, and Blacksky community disagreed with that ban. When Blacksky switched http://blacksky.community app to have its own complete stack (including its own database), that person’s posts became visible there (despite them being banned on Bluesky app) because they reversed that moderation decision. This was possible because the data for this person’s posts still lives on their PDS.
In general, the data being “pulled outside” products is what enables new products (or forks of products) to come onto the scene and immediately begin competing because they don’t have to solve the “cold start” problem. If you log in, all your stuff is “already there”. And it’s the same shared world so the community doesn’t get forked. You’re just looking at the same underlying data under a different lens, and products act like lenses rather than boxes.
This doesn’t mean that “censorship” can’t exist (every layer can ban you, as always) — but it means that every layer of the stack has opportunity for competition that isn’t possible with centralized platforms. In fact, arguably, it’s more flexible than a Mastodon instance because you can’t fork a Mastodon instance “with all its users” and offer a version that reverses some moderation decision. In atproto, you can.