One of the obvious things about Merkle ledgers is that everyone can have their own. You could have one per tradeable instrument on an exchange, for example. Anyone can start an altcoin; why not the BoE?
The proof-of-waste system allows the system to be fully distributed by continuously burning electricity such as to push up the minimum cost of overwriting some other node's choice of doublespend (note: NOT ability to forge transaction!) to very high levels.
If you discard the "distributed" requirement, you can save a lot of electricity by having a single or multiple CA-like series of authorized stamp-issuers. It then looks a lot more like Chaum's digital cash.
If you discard "pseudonymous" as well, noting that bitcoin pseudonymity is both fragile and directly contrary to KYC/AML, you can make further optimisations.
signature verification, P2P, cryptographic hashing, public-key cryptography
Old, but not yet widely deployed outside of the browser-CA system. Getting banks to use proper digital signature technology would be a major upgrade.
(Also, remember in the UK we have both EMV and "faster payments", so the US problems of stolen magswipes and waiting for cheques are not so prevalent.)