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The actual build date doesn't matter if the software is reproducible - but its a proxy for 'how out of date is this software'.
If you actually had reproducible builds, the build date would not tell you anything about how out of date the software is—you would only need the date of the source code the binary was built from.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.
The actual build date doesn't matter if the software is reproducible - but its a proxy for 'how out of date is this software'.