You're wrong. Most enterprise blockchains use BFT algorithms or even round-robin instead of mining. What they are after is a highly auditable shared computing environment.
The use of PoW isn't what makes a block chain a block chain. The idea is that you don't have a single trusted party you have a collection of them that need to collude to cause harm to spread the required trust.
But if you have some trusted party just use a DB.