Raw training data is raw. A really big model trained on it has already done a first-pass of finding patterns and squeezing out redundancy. Re-ingesting the full training set to train a smaller model is probably more expensive, for marginal quality improvement over distilling from the large model.
Distilling from a larger model is not only probably cheaper than from data, it's also likely higher quality. There's pretty strong support for the proposition that NNs learn a smoothed and regularized version of the data. The NNs are likely higher quality than most of the data they are training from.
