Why do Linux/POSIX have lchown but not lchmod?

Linux, like most Unix-like systems (Apple OS/X being one of the rare exceptions), ignores permissions on symlinks when it comes to resolving their targets for instance.

However ownership of symlinks, like other files, is relevant when it comes to the permission to rename or unlink their entries in directories that have the t bit set, such as /tmp.

To be able to remove or rename a file (symlink or not) in /tmp, you need to be the owner of the file. That's one reason one might want to change the ownership of a symlink (to grant or remove permission to unlink/rename it).

$ ln -s / /tmp/x
$ rm /tmp/x
# OK removed

$ ln -s / /tmp/x
$ sudo chown -h nobody /tmp/x
$ rm /tmp/x
rm: cannot remove ‘/tmp/x’: Operation not permitted

Also, as mentioned by Mark Plotnick in his now deleted answer, backup and archive applications need lchown() to restore symlinks to their original owners. Another option would be to switch euid and egid before creating the symlink, but that would not be efficient and complicate right managements on the directory the symlink is extracted in.