Asymptotically, minimizing the AIC is equivalent to minimizing the leave-one-out cross-validation MSE for cross-sectional data . So when we have AIC, why does one at all use the method of dividing the data into training, validation and test sets to measure the predictive properties of models? What specifically are the benefits of this practice?
I can think of one reason: if one wants to assess the models' predictive performances, out-of-sample analysis is useful. But although AIC is not a measure of forecast accuracy, one usually has a good idea if some model is reaching its maximum potential (for the data one is given) in terms of how well you are gonna be able to predict.