This is one of the reasons the scientific method blossomed: objectivity, rigor, transparency, reproducibility, etc. Black boxes can lead to bad decisions because it's difficult to question the process leading to decisions or highlight flaws in conclusions. When a model is developed with more rigor, it can be openly critiqued.
Instead, we have models running across such massive datasets with so many degrees of freedom that we have no feasible way of isolating problems when we see or suspect certain conclusions are amiss. Instead, we throw more data at it or train the model around those edge cases.
To be clear, I'm not saying ANN/DNN models are bad, just that we need to understand what we're getting into when we use them and recognize effects that unknown error bounds may cause.
If, when the model fails to correctly classify a new data point, the result is your photo editing tool can't remove a background person properly... then so be it, no harm no foul. If the result is that the algorithm classified a face incorrectly with high certainty and lands someone in prison as a result (we're not there, yet) then we need to understand our method has potential unknown flaws and we should proceed carefully before jumping to conclusions.