Strictly speaking, blockchains are closer to
logs than arbitrary databases, because we need strict ordering of events in blockchains. The distinction between blockchain and distributed logs isn't binary, but exists on a spectrum. It's all about the
threat model.
PoW consenus that you see in Bitcoin has extreme adversarial assumptions. Raft is on the other side of the spectrum; it's just bare-bones state machine replication and simply trusts the elected leader.
The thing is, your adversarial model can lie somewhere in between these extremes. That can be the case for bank networks or supply-chain management and isn't necessarily inefficient (Hyperledger Fabric). I'm not really familiar with private blockchains, I think they are just a rebranding of public key infrastructure.
I personally think permissionless DLTs are much more interesting, and actually deliver on our expectations of decentralization. Whether certain flavors of PoS will be sustainable is yet to be seen.