I realized this is misleading as an answer to your question, but it's too late to edit. Block producers (i.e. miners) don't need to keep track of chain state, b

I realized this is misleading as an answer to your question, but it's too late to edit. Block producers (i.e. miners) don't need to keep track of chain state, but provers need to know the state of block n-1 to generate a proof for block n. In practice, the current state is pretty small, but admittedly way more than 22KB: I just synced a node and its data directory is 235MB. The zero-knowledge proofs still provide the advantage that historical state doesn't need to be kept by anybody: if news of a better chain tip comes along (including while bootstrapping), it'll come with a recursive proof of its validity, whereas with Bitcoin et al. it'd need to check if it's building on a valid block (and thus keep at least the hashes of previous blocks).