[aeijdenberg]

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/

[mistermumble]

But if you can accept centralization, then why not just use a conventional DBMS? (This is a real question, not a rhetorical argument.)

[aeijdenberg]

So that you (or other interested parties) can verify the correct operation of the centralized authority, and so that the central authority can prove that they aren't hiding anything.

For example, in the case of certificate transparency, that the CAs aren't mis-issuing certificates, and further that the logs aren't conspiring to hide entries (such as via split views).