> One naive belief many people have is that proofs should be "intelligible" but it's increasingly clear this is not the case.

That's not a naïve belief. Intelligible proofs represent insight that can be applied to other problems. If our only proof is an opaque one, that means we don't really understand the area yet. Take, for example, the classification of finite simple groups (a ten-thousand-page proof): that is very much not a closed area of research, and we're still discovering new things in the vicinity of the problem.