Hate to quote myself, but Lamport is able to establish a meaningful logical clock by the participants of the system interacting, I suppose this might be considered PoW, but does it have to be someone mining? Would the time network fall apart if only one or two systems were a part of the network at some point in the future?
It only works if everyone in the system is honest. If you use the assumption that everyone is honest, you might as well just randomly pick a single node to tell everyone else what the time is.