>> Ok, I could add display-sort-function directly to the imenu completing-read
>> that will depend on the value of display-sort-function.  Then there will be
>> no need to change the manual.
>
> Except we should then remove the reference to "menus", right?  Because
> if you do that, the customization of sorting order will affect both
> the menus and the completion, right?

Indeed, this will require removing the reference to the mouse menus.

But when I tried to use imenu-sort-function for sorting the completions,
I found a problem that makes such change impossible.

The problem is that the default value of imenu-sort-function is nil.
This means that by default the items on the mouse menu are unsorted.
But the completions are sorted, and we can't change this default
behavior.  Therefore, imenu-sort-function can't define how the
completions are sorted.  So this is just a documentation task
that is done in this patch: