@civodul @jas4711 A somewhat relevant example is how the NEWS file is checked, but there are other examples.
As for “and distributions could package the gnulib git repository (up to some current version)”, I’m not sure it would be easy, because git allows itself to re-pack its objects whenever it wants, so further steps may be needed for the content of the .git repository to remain reproducible over time.
@civodul @jas4711
Finally, I think we should not forget that the modification time of the .texi file impacts the modification date that is printed in the final output of the manual. Setting it to 1970 is awkward in this case.