An individual person's data under the AT Protocol is a signed chain of operations. A repository host is expected to always serve the most recent version of the repository to anyone who asks for it. The repository can survive the death of the host by being transferred to another host, and any responsible host is expected to facilitate these transfers. Repositories are also likely to be backed up in distributed storage, so even when hosts don't actively facilitate transfers, their state will basically always survive them.
The expectations placed on hosts correspond fully to the special features that allow blockchains to play host to decentralized finance, only instead of being proved by cryptography and game theory, they're going to be not-quite-proved by organizational incentives, monitoring, and possibly government audits and legal obligations, which are not as strong as proofs, and many in crypto would argue that they're not sufficiently strong for AT Protocol to be applicable to finance, and especially not strong enough for the AT Protocol to be preferred over other ledgers.
However, the AT Protocol has 6 million users (bluesky), and it has no scaling limits (consensus only requires checking in with a set of hosts who you trust not to collude).
No one plans for the AT Protocol to develop into a finance host, but it's almost inevitable that someone will build that functionality. And everyone will say, "Don't use the smart contract extensions, it's not as secure as a real ledger, and the trust model makes it prone to centralization," and even AT's authors might be saying this. But some people will use it for finance anyway, and then there will probably be no attacks on any major hosts, and people will keep using it for finance, and eventually enough people will be using it for finance that it'll settle over people that we didn't ever strictly need cryptographic or game theoretic proofs to build a system of computers that could be trusted to faithfully perform computations and serve most recent state. Human organizations can basically do that well enough.
Or, that could happen, as far as I can tell. I'm not sure whether it will. Place your bets.
Early close conditions:
NO: If ATProto is clearly dead, deprecated by another distributed social network protocol. (In which case I might make a market about that protocol instead)
NO: when a proper ledger with negligible transaction costs and good interoperability with AT (or its apps) gains mass adoption. This would signal that there is no need for ATproto to become a distributed ledger, so even if it happens after that point, it like, doesn't matter, it might as well not have.
YES: when the AT smart contracts thing is built and people are using it for finance and the userbase is definitely collectively storing over 7bn (inflation adjusted from August 2024) USD of assets on their PDSes.