If you can accept centralization (which for many non-crypto-currency use-cases actually makes sense, since it mirrors the way the real world works) - you don't actually need proof of work.

You can still get the benefits of verifiability, append-only, detect misbehavior etc without it. See for example Certificate Transparency (RFC6962) for a standard that implements those properties using similar Merkle Tree constructions.

Disclaimer, I have a startup that generalizes the same Verifiable Logs (and also allows for Verifiable Maps): https://www.continusec.com/