>>   (outline-minor-mode-cycle--bind map (kbd "TAB") #'outline-cycle)
>>
>> Maybe this requirement should be documented in the docstring
>> and mentioned in NEWS?
>
> I think this is a good idea since people who have already keys bound
> on outline-minor-mode-cycle-map are likely to be as surprised as I was.
>
> But I also think that it is more important to mention this in the
> docstring for outline-minor-mode-cycle-map. Since its current
> docstring "Keymap used by outline-minor-mode-cycle." is misleading in
> my opinion, especially since any key there is going to be active
> if outline-minor-mode is on, regardless of the value of
> `outline-minor-mode-cycle`.

Thanks for suggestions.  The following patch addresses all the points
that have been raised, except obsoleting `outline-minor-mode-cycle-map`.
It's more convenient to bind keys in this map since `outline-minor-mode-map`
is not explicitly defined unlike `outline-mode-map`.

> Also I was confused by the two hyphens in the name
> outline-minor-mode-cycle--bind and thought that it was a private
> function even though in retrospect they are in the wrong place
> for it to be private.

Two hyphens in the name rather indicated that the implementation
is subject to change without notice - an assumption that is true
for internal functions.  So now I'm not sure if adding an alias
without two hyphens is worth to do.