But something I haven't understood is that nix compiles to derivations. I don't think it would be difficult to have a nix compiler that takes Lisp or whatever and spits out derivations. It would be able to use stuff from nixpkgs as well, at least partially anyway.
The built derivations are an extremely simple format anything can produce.
This is originally how Guix worked— it generated .drv files in the same format as Nix and then asked a Nix daemon to build them. But both projects consider the derivation format an implementation detail that should be free for them to change according to the needs of the rest of the stack, rather than a stable interface for downstream consumers (be they end users or other software tools).
The above is not just theoretical— as a result, the derivation formats of the two projects have diverged.
(Tbh I agree with their position, though. I don't think the concept of the derivation should really be visible to end users. The way the term is used is extremely overloaded/ambiguous, and so at the end of the day it's jargon that serves more to obscure than to teach.)
I've been using lisp for over 20 years now and would much prefer if guile replaced the nix language (or Common Lisp, if I can dream), but I still use NixOS for practical reasons.