I guess the question would be: if you don't trust a central authority to keep that database immutable and add records honestly, how do you design a distributed solution?
Blockchains are pretty much just an append-only log, but they were the first decentralized answer to the double-spend problem. So I'm not sure it's a case of what blockchains can do that immutable databases can't - they're a way of implementing decentralized immutable databases.
By this definition, ethereum is not a blockchain[0]
> they were the first decentralized answer to the double-spend problem
Physical reality is decentralised answer to double-spend problem (the gold molecules 'exist' in your hand, no centralised god manifested it but physics worked on universal matter in a decentralised manner). The 'problem' is created when we assumed centralised trust is even possible.
A blockchain is decentralised answer to double-spending a 'non-physically interactable' good(don't mean 'virtual' because POW is real).
[0]https://ethereum.stackexchange.com/questions/9535/how-does-a...