A blockchain is a distributed ledger, not necessarily public, although bitcoin, being the most famous, is public.

In this implementation it seems anyone can read the blockchain, but writing to it is permissioned/controlled.

It is a private, yet decentralized, ledger. This can have many use cases; for example a ledger could be shared between a network of financial institutions, without one of these institutions getting to be the single source of truth. It could also be used by for example a nation state to make parts of its financial system transparent to the entities to which it holds relevance.

All in all, it in many ways mitigates the need for trust between the systems participants, just like what is the purpose of the block chain in the case of for example bitcoins.