ℹ️ I've submitted the detekt CLI as a Nix package (currently it's made it only into the unstable channel):

$ nix-shell -p detekt -I nixpkgs=<https://github.com/NixOS/nixpkgs/archive/f80ac848e3d6f0c12c52758c0f25c10c97ca3b62.tar.gz> --command 'detekt --version'
1.22.0

Added to detekt's website https://github.com/detekt/detekt/pull/5757