Monetary theorists have struggled for decades if not centuries to explain why we use and value money. Modern theory, which needs to be more explicit about its assumptions, has highlighted how silly some axioms of monetary theory are. For example, why would money make any sense in a utility function when future consumption is already taken into account? Or what about cash-in-advance in quarterly models of the business cycle. Money search model bring progress to the table as they model the problem of the absence of double coincidence of wants, although still with some rather crude assumptions. But at least it is going in the right direction.
Andrew Clausen and Carlo Strub come up with a new motivation for money. Suppose that there is a fix cost in production. Unless you want to produce at full capacity every period, you will then choose to close all operations from time to time and take a vacation. But you must live from something when you do not work and you have no savings technology. This is where money comes to the rescue. Without it, it would have been impossible to smooth consumption across periods, and thus money is valued and welfare enhancing. But beyond the possible elegance of the model, is anybody actually believing this story? I do not think in makes sense to discuss the intertemporal allocation of resources in a world without assets, especially if you want to apply it to anything modern.