Due to spurious correlations, it could still be helpful for the insurance assessor so that they can use bias mitigation techniques. Otherwise, it might learn something about zip code or something else that leads to a similar outcome as having race as an input variable. Just removing a sensitive variable does not suffice for preventing unwanted bias.
Then you are confusing bias with bias. One is data bias and the other one is racial bias. If you remove the data bias, you are by definition introducing a racial bias by imposing your will on reality.
For example, a medical screening NN may find race to be a valuable feature for the prediction of illness; but a health insurance assessor should not.