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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.

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I think this is accurate but mostly because statistical modelling aims for interpretable parameters. That very strongly regularises complexity.

I think they have totally different goals typically. For example, let’s say we are doing a sampling procedure. How do you estimate the sampling error? I’m not aware of a machine learning technique that will help, but you can use Bayesian and MCMC techniques

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