So, I disagree with the "inherently racist" portion of your argument. You can evaluate the classifiers in a race independent manner, i.e. take a look at the metrics stratified across race. I'm going to proceed here assuming that the classification task is possible.

Say in your example of criminality, if black people were more predicted by the classifier, it isn't racist if it accurately reflects the base distribution. There's a line to be crossed here, and to me it's if that application starts to significantly (where the boundary lies here is up for debate), and directly affect the non-criminal portion. I'd say that if the misclassification error is similar across racial lines, then there is no issue.

Additionally, I don't quite agree with the "making racial biases worse" argument either. The way I see it, we already use racial heuristics in law enforcement. With automated, replicable tasks, we can at least quantify the degree of bias and correct for such.