Hume's problem of induction is not about deriving moral principles (I believe you got it confused with the "is-ought" dichotomy.) Most philosophers have largely given up on giving a rational deductive basis for why we should believe in induction, so if anything that seems to be a perfect example of what you're describing.

I don't think the nature of quantum reality is anywhere near as settled. For decades, we thought that it was impossible to test local hidden-variable theories. Thank god some people were still working on the problem!