Full Title: Is there a balance to be struck between simple hierarchical models and more complex hierarchical models that augment the simple frameworks with more modeled interactions when analyzing real data?

Well, my impression is that the statistic paradigm itself limits the complexity of a model through it's basic aims and measures. Especially, a statistical model aims to be an unbiased predictor of a variable whereas machine learning/"AI" just aims for prediction and doesn't care about bias in the sense of statistics.

"When working on your particular problem, start with simple comparisons and then fit more and more complicated models until you have what you want."

sounds algorithmic...