It's the moral equivalent of making major headway against P!=NP; or, proving that there are no global hidden variables in QM; or, that there's a clear path ("just engineering") to room-temperature semiconductors.
I feel like saying this is similar to making progress on P!=NP is not accurate (extreme disclaimer: I have no formal math training). My understanding of P!=NP is that an answer to that has strong implications for the nature of the concept of determinism _of reality_, let alone most cryptography and lots of other stuff too. From my quick scan of the GRH wikipedia article, it doesn't appear that the GRH has the same widespread almost philosophical implications as P!=NP.
I think P != NP is extremely interesting, but I wouldn't say it has strong implications for the nature of the concept of determinism or reality. I think that the idea of a Turing machine / the notion of computability has deep philosophical implications, but even that I wouldn't say has implications for "the nature of reality."
If you think that prime numbers are interesting, then I can tell you that GRH is the single most central conjecture in the study of prime numbers. Personally, I think prime numbers are some of the most fundamental and intrinsically interesting objects in pure math, but of course, this is subjective!
