I thought a major argument for double-entry bookkeeping was for error detection and correction/auditing. Was I mistaken? It was sold to me like that many years ago.
We have technology that will help with that (signing, hashes, parity bits, blockchain, etc) but none of that matches the simplicity of a notepad in a desk at a local takeaway store.
Yes, that's the classic argument. However, it is quite irrelevant today, where human error and time are both stupendously more expensive than precise record keeping executed by software in the first place.
The tools you mention are tangential to this: signatures are for non-repudiation and authenticity, hashes are for checksums, parity is for self-repair in bad checksum cases (rarely used in application level software today), and blockchains are for distributed trust (eg. distributed ledgers), essentially providing the combined properties of signatures and hashes to a shared database in a distributed system over time.
Note that all depend on the input of valid data in the first place, and none can be efficiently applied to a manually written notepad.
We have technology that will help with that (signing, hashes, parity bits, blockchain, etc) but none of that matches the simplicity of a notepad in a desk at a local takeaway store.