I don't really agree with you.
> If you were rejected by a bank for a home loan, you would want to know why your creditworthiness wasn’t evaluated positively (and banks must explain precisely why to regulators).
This is why we don't use humans to evaluate credits, but precise algorithms. Humans are just applying the algorithms, they are not evaluating themselves with their gut feeling. I don't see why this would change with AI. Regulations prevents unexplainable tools to be used there, so deep learning black box models will not be used, similarly to why humans are not used today.
But in cases where performance is required, but not explainability, then deep learning will strive. And I believe that cases where explanation is required is only a very small subset of areas where AI could be useful.
> And if a self-driving car made a decision in a collision
Would you prefer a car that crashes once every 100 million miles but is not explainable, or a car that crashes once every 100 miles but is interpretable can explain why it crashed ?