I don't think the blockchain walk has to be done locally. Much like someone looking up DNS records don't need to participate in the DB management to get their records, there can be intermediaries which provide the response and still rely on the blockchain as a source of truth?
The value of the blockchain (in the context of name resolution) would (should) be limited to enabling trustless-ness of the response. I can cryptographically authenticate the origin of the response. If you don't trust that source, zk proofs would enable the user to validate the response is part of the latest version of the blockchain's state without looking at all of the history.
I think the cost of carrying the whole history is a red herring.
> there can be intermediaries which provide the response and still rely on the blockchain as a source of truth
But then you have to trust the intermediaries. You can verify their claim, but doing so is so costly it's what made you turn to intermediaries in the first place.
> I can cryptographically authenticate the origin of the response.
A blockchain is not needed for that, certificates can do that.
> zk proofs (…) the latest version of the blockchain's state (…) cost of carrying the whole history
Knowing enough information about the latest version of a blockchain's state to validate responses would require either that you trust the third party which would provide the hash of the last block to you, or that you follow, blocks after blocks, what's added to to ledger, verifying each block's integrity and all. I'm not saying that's not doable, but that it either requires some boot-up time or to be online all the time; i.e., it more or less amounts to running a node which is what we seem to agree is not something most people / end devices will do.
You should be able to cryptographically prove a) the block height of the current block and b) the state of any account, in constant space, using zero-knowledge proofs.
You don't need to trust a third party and do not need to be online all the time for that.
The value of the blockchain (in the context of name resolution) would (should) be limited to enabling trustless-ness of the response. I can cryptographically authenticate the origin of the response. If you don't trust that source, zk proofs would enable the user to validate the response is part of the latest version of the blockchain's state without looking at all of the history.
I think the cost of carrying the whole history is a red herring.