You could maybe get away with saying that we're fairly confident that _at some point_ we'll be able to accomplish such a feat (translating all interesting problems into scientifically decidable ones), but even that would be a super hairy/controversial assertion.
Same thing is likely to hold vis-a-vis neuroscience and philosophy of mind.
I suspect it couldn't be a physics result, because the question is something like "Why does the universe follow natural laws at all" and/or "what IS a natural law, in metaphysical terms" ?
Who is "we"? Americans? Because continental europeans very much care.
Well, if by tiny you mean a good 5-10%, then yes. Besides, when was that number much higher?
Did you notice the constraint:
> we generally don't particularly care about what they have to say anymore.
It's a human perspective way of saying it's not relevant to much the active work, but it still is being worked.