A blockchain is just a data structure. That description is more befitting of Decentralized Finance/DeFi
What would be the advantages of using a private, permissioned blockchain over a MySQL/Oracle/SQL Server database for storing data?
Why as an external user would I trust a centralized blockchain more than I would trust a centralized database? They are both private owned and controlled by a company.
As an external user? Nobody cares, it's not for you, move on.
And why couldn't a distributed SQL database be append-only, immutable, time-stamped, and implemented so each new entry has a hash of the previous state? (If you own it, just set it up to disallow updates or deletes, and allow inserts only through a trigger / stored procedure that adds the timestamp and hash.)
I recently read about a steel maker in India executing a cross border order on blockchain. On further reading it turns out their bank used a third party company for digitizing letter of credit and that company claims to be using an enterprise blockchain R3 Corda. R3 itself is owned by a consortium of banks and on their website they don't use the word blockchain to describe Corda. They call it DLT.
My understanding is that a blockchain is supposed to be distributed, trustless, permissionless, immutable and open. At least that is what the core ideology behind it and is touted as the cornerstone features of blockchain. An enterprise blockchain is private, trustful, permissoned and everything that is a blockchain is not supposed to be. At that stage is it even a blockchain or just another propitiatory data store?