The option to self-host your identity piggybacks on the DNS-system. A certain domain name resolves to the server where you store your ATProto identity. As long as you control the domain name, you control your identity. The ATProto identity is simply a pointer to where you currently store your data that your followers/contacts can use to find your content (IIRC).
The non-selfhosted alternative is a central identity service run by Bluesky. Unfortunately, the identity cannot be moved for obvious reasons. It would be good if there were some more options there. In principle, if the ATProto identity was tied to the government identity, that would make it moveable and non-hijackable. For some people, celebrities and such, that would be a good option.
Regardless of whether you selfhost your identity, you can selfhost a Personal Data Server (PDS), which stores your data and makes it available to the network. The PDS can move, cause that's what the identity is for.
Feeds and other stuff is again independent.
The company Bluesky Social PBC created the microblogging service Bluesky and the ATProtocol. It's like the company Mastodon created the microblogging service Mastodon. There are other services built on ATproto that are EG like Reddit/Lemmy. But these have not taken off significantly.
The ecosystem is mature enough so that you can participate in Bluesky without using services offered by Bluesky Social PBC and without making sacrifices. For the most part, you can move without abandoning your account.
It is true that the servers are mostly run by the Bluesky company, but so what? Email is mostly run by Google and no one seems to think that's a problem.