People shouldn't use git without having configured that. It would prevent incorrect commits landing in public repositories. Actually git defaults to some made-up local git author if it's not set, and that's less useful and sometimes invalid, provoking git-fsck errors.
Git explicitly shows a "Committer" line when typing the commit message if it chooses a default, so I also find not setting one globally and getting this reminder to be more useful:
# Please enter the commit message for your changes. Lines starting
# with '#' will be ignored, and an empty message aborts the commit.
#
# Committer: Ben Alpert <balpert@balpert-mbp.local>
#
# On branch master
# Your branch is up-to-date with 'origin/master'.
#
I agree. A potential middle ground would be a small button that lets them skip that screen with a second confirmation dialog box with a warning about it.