I think build reproducibility is a cargo cult.Most people here are debating you on the security angle, but in the case of Nix (and Guix) there is another important angle - reproducible builds make a content-addressed store possible.
In Nix, the store is traditionally addressed by the hash of the derivation (the recipe that builds the package). For example, lr96h... in the path
/nix/store/lr96h3dlny8aiba9p3rmxcxfda0ijj08-coreutils-8.32
is the hash of the (normalized) derivation that was used to build coreutils. Since the derivation includes build inputs, either changing the derivation for coreutils itself or one of its inputs (dependencies) results in a different hash and a rebuild of coreutils.
This also means that if somebody changes the derivation of coreutils every package that depends on coreutils will be rebuilt, even if this change does not result in a different output path (compiled package).
This is being addressed by the new work on the content-addressed Nix store (although content-addressing aws already discussed in Eelco Dolstra's PhD thesis about Nix). In the content-addressed store, the hash in the path, such as the on above is a hash of the output path (the built package), rather than a hash of the normalized derivation. This means that if the derivation of coreutils is changed in such a way that it does not change the output path, none of the packages that depend on coreutils are rebuilt.
However, this only works reliably with reproducible builds, because if there is non-determinism in the build, how do you know whether a change in the output path is changed as a result of changing a derivation or as a result of uninteresting non-determinisms (the output hash would change in both cases).