$datadir/doc or $docdir is not necessarily the right location to place
the COPYING file. Some distributors might want to install it somewhere
else. eg., Fedora RPMs [1] mark the license text with %license which
puts it under $datadir/licenses. Currently, such a distributor has to
go out of its way to not have two copies of the files.

As a data point, GLib doesn't install its COPYING file either.

Users can still see the license from the application's about dialog.

[1] https://fedoraproject.org/wiki/Packaging:LicensingGuidelines