A general way my mental model of how statistics works disagrees with what you write here is on whether the specific properties that are in different contexts required of estimators (calibration, unbiasedness, minimum variance, etc.) are the things we want. I think of them as proxies, and I think Goodhart’s law applies: when you try to get the best estimator in one of these senses, you “pull the cover” and break some other property that you would actually care about on reflection but are not aware of.
(Not answering many points in your comment to cut it short, I prioritized this one.)
A general way my mental model of how statistics works disagrees with what you write here is on whether the specific properties that are in different contexts required of estimators (calibration, unbiasedness, minimum variance, etc.) are the things we want. I think of them as proxies, and I think Goodhart’s law applies: when you try to get the best estimator in one of these senses, you “pull the cover” and break some other property that you would actually care about on reflection but are not aware of.
(Not answering many points in your comment to cut it short, I prioritized this one.)