How would a centralized block chain work?
Sure. You just use a database that keeps track of who has how much money. You can do this any way you want. You don't need anything fancy like POW, POS, or even a blockchain. The only reason you would need or want these things is to permit decentralized operation without a central authority. If you are the central authority, what you say is law just because you said it. So no need for anything fancy.