As a NixOS user for 3 years, and a Claude user for 1+ year, I agree with you that it's an ideal fit. I've been very happy with, for example, how Claude can configure GNOME via dconf settings: tweaking those settings declaratively requires cross-domain knowledge and knowing where to dig. But Claude just knows.
But trying to set up an environment for one of those perpetually running AIs, and asking it to refactor its own configuration according to some of the high-level abstractions like dendritic flake-parts, and so on, it's just clueless and will improvise without success.
What makes Nix hard for humans also makes Nix hard for AIs: Untyped lambdas that get resolved in some implied out-of-file context means you have to know if you're looking at a NixOS module, a home-manager module, a nix-darwin module, a flake-parts module, and so on. And those modules may make assumptions about what's imported in the parent scope.
So I feel like you need to supply a rather extensive context for your project that details how you want things structured, because the ecosystem is quite fragmented, people don't fully agree on what good patterns are, and so the AI can't know what the good patterns are.
Just to be absolutely clear: I think that supplying an extensive context is absolutely worth it, and I'm having great joy and success building better Nix-based project templates, Nix-based deployment templates, etc. The amount of stable, well-made projects made by other Nix users is just amazing.