Part of your Bluesky identity is recorded as a DID, a kind of secure universal identifier, and to be accessible at all times, your DID has to be registered and stored on a registry. That's similar to how websites have to register their domain names with one of a handful of for-profit registries, and in fact, Bluesky handles are all domain names. So big question #1 is: Who gets to act as a DID registry? Because they will, in effect, hold the keys to your whole identity on the network.
In principle, you could provide your own domain, and that handle would be yours to port around as long as you continue to pay for it, like any other TLD. In practice, though, most social media users aren't going to pay for their own domain. They'll use a subdomain provided by a service. The protocol assumes that service will be independent of the PDS, but AFAIK that's not required. So maybe a PDS going offline actually COULD take a bunch of accounts with it. We'll see how it's implemented.