if you have a reproducible build, then the notion of "software was built on date by user" is kind of useless information, no? Because it does not matter - if you can verify that a specific git hash of a codebase results in a particular binary through reproducible builds, a malicious adversary could have built it yesterday and given it to me and i can be almost surely confident (barring hash-collisions...) it's identical to a known trusted team member building it.
Having information about which git has was used, as well as the time it was published, is part of the source distribution so an output can contain references to these inputs and still be deterministic w.r.t. those inputs.
If you REALLY want to know when/who built something, you could add in an auxiliary source file which contains that information, which is required to build. Which is essentially what compilers which leverage current time do anyway, it's just implicit.
The usecase is: user wants an easy way to know, from the GUI of some running software, exactly what build/version/git commit/branch/date they're running - perhaps to file a bug report for example.
The actual build date doesn't matter if the software is reproducible - but its a proxy for 'how out of date is this software'.
If you actually had reproducible builds, the build date would not tell you anything about how out of date the software is—you would only need the date of the source code the binary was built from. By definition, the binary you'd get from building a version of the source today would be identical to the version you'd get building it the day that version of the source was finished.
Your source would also have to have a reference to which exact version of which compiler to use, which versions of which external headers to use, etc. and now you're inventing Nix.
Conceivably there could be a standard for a sidecar file to specify how something was built (e.g. nixpkgs commit hash, or all of the parameters that went into the build). Or content address the inputs, i.e. invent Nix again.
So we could solve this problem by having everyone standardize on using Nix.
Having information about which git has was used, as well as the time it was published, is part of the source distribution so an output can contain references to these inputs and still be deterministic w.r.t. those inputs.
If you REALLY want to know when/who built something, you could add in an auxiliary source file which contains that information, which is required to build. Which is essentially what compilers which leverage current time do anyway, it's just implicit.