Update: Looks like I'm wrong.

I disagree: just because someone tried it once and got a useful error message doesn't change the fact that $! is not documented to be defined at this point.

$! may well get set differently (or not at all) in different circumstances, when testing different files, or on a different O/S, or depending on phase of the moon for all we know.

Your suggested clearer error messages are definitively more correct; the only change I might make (at the risk of getting too clever) is to avoid the duplication with something like:

  die "$_ is not a valid directory\n" for grep !-d, $srcdir, $destdir;
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Hugo