... and in fact, it's machine learning models whose performance is tested using cross-validation or a holdout sample that assume new points are drawn from exact

... and in fact, it's machine learning models whose performance is tested using cross-validation or a holdout sample that assume new points are drawn from exactly the same distribution that generated the training data, whereas Bayesian priors are often used for the exact opposite purpose: when you're afraid the data is too noisy or unrepresentative and won't generalize without incorporating outside information. Also, there is no need to train any model whatsoever if your prior is correct. The prior is the model.