What? What would be the point of a non-distributed blockchain? Fundamentally, blockchains are a solution to the distributed consensus problem, where you're not guaranteed anything on the length of time it takes to communicate between two nodes. Also known as asynchronous consensus.

If you're local (or within a small network with bounded, you don't really need asynchronous consensus. Dolev-Strong or any number of other synchronous/semi-synchronous protocols would work fine.