for pgm in $( dpkg -L coreutils | grep bin | sed 's,^.*\/,,' ); do man $pgm 2>/dev/null | sed -ne '6p'; done
whatis -s1 $(dpkg -L coreutils | grep "bin/" | sed 's,^.*\/,,')
Note that your solution skips chroot (man section 8). The fix:
whatis -s1,8 $(dpkg -L coreutils | grep "bin/" | sed 's,^.*\/,,')
whatis -s1 $(rpm -ql coreutils | sed -n 's,.*/bin/,,p')