> A black box oracle that just tells you whether statements are true or false is not the goal of mathematics and would not be particularly interesting to the field
This is a crude distortion. The recent breakthroughs have come with proofs, reasoning and verification, and there is no proposal that I'm aware of that would do away with these foundations. There's also some rather ugly solipsism in the idea of keeping what interests the field as a limit. Mathematics has broader relevance to humanity than merely to please and support mathematicians, and if other fields can make practical use of profound well-proven future math, mathematicians will have a hard time making a case that their comprehension must come first.