Correlation between outcomes and race, gender, etc. is NOT bias per se. And yet that's what almost all claims of discrimination by machine-learned models are based on.
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It seems like the issue is that reducing everything to MSE/accuracy is simplistic and dangerous. Policies are often shaped by what we would like our societies to look like in the future, not only by how they look like right now or in the past.
The model's job is to be accurate. The place for political and social considerations is in the decision system that uses the model. Otherwise we're distorting reality to suit our ends.
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I think that the job of a model is much more than just being accurate. It needs to help us solve issues. Great if it is accurate *and* can help us fix our issues. Why should I care about a super accurate black-boxy binary answer, say?
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I do not think I disagree with you that incorporating our own biases into the system is a good idea. But I think that "system design" is tremendously difficult, and accuracy is only a very small part of a successful solution.
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