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In previous discussions here of statistical bias, you have considered cases where bias may be acceptable because of trade-offs. But in some other cases, e.e. the Poisson distribution parameter estimation, an unbiased estimator is obviously absurd, e.g. giving negative estimates in some cases when the parameter value is positive. The maximum likelihood estimator is a far better choice for common purposes, and of course it is a biased estimator.

Do you think cases where the maximum likelihood estimator differs from the unbiased estimator, or where the unbiased estimator is plain absurd, have any relation to the non-statistical sense of bias, and if so do you have any thoughts on bias in those cases?

I think there's substantial overlap between some of your ideas here and Richard Gabriel's famous "Worse is Better". He wrote several follow-on essays, too, all linked to from there. You might want to have a look at them.