The Traveling Wilburys-like quartet of economists Abadie, Athey, Imbens and Wooldridge have a nice paper on this in the context of causal inference and robust standard errors. To summarize and simplify, these standard errors capture the fact that even if we observe outcomes for all units in the population of interest, there are for each unit missing potential outcomes for the treatment levels the unit was not exposed to.
What does all that mean? For example, suppose you want to figure out what the effect of legalized marijuana on pizza sales. You're comparing sales per capita for Washington and Colorado to all the other states. The standard errors reflect that you haven't observed the state of the world where Washington and Colorado did not legalize and the states of the world where other states legalized first. Other times you want to extrapolate your estimates to the future, which you have also not observed. In all these cases, you only have a subset of the full population and so the standard errors of the causal estimate reflect that sampling variability.