>> Thanks, I think your idea is correct.  But I'm not sure if
>> minibuffer-completion-help is the right place for wrapping in
>> with-minibuffer-selected-window.  This means that all calls of
>> annotation-function will be in the original buffer, whereas
>> only read-extended-command--annotation needs such wrapping.
>
> Oh, that's a very good point. Probably it would be best to leave
> minibuffer-completion-help as is, and change only
> read-extended-command--annotation.
>
>> Or do you care that such wrapping will be called for every command
>> in read-extended-command--annotation?  Then instead of annotation-function
>> you could try to use a new function affixation-function that is called
>> only once, so you could add wrapping to it.
>
> My Emacs doesn't have affixation-function yet, so I don't really know
> anything about it.

I'm sorry that your version of Emacs is not updated too often.
So here I created a patch based on current master, and after
pushing it, sometimes it will arrive to your updated version.