>> Actually, we can do better.  I will soon install a simple change that 
>> fixes the problems discussed in this bug and in all the related 
>> discussions I'm aware of.  We can then take it from there, if some 
>> issues remain.
>
> Done.
>
> I will wait for a week or two for reports about things this change 
> breaks, or about issues still left to be fixed after this commit, and if 
> nothing surfaces, I will close the bug report.
>

Alas...

See the two attached screenshots, taken with (setq max-mini-window-height 
1) and icomplete-mode.  "no-completion-candidates" is what a user will see 
with your change, "completion-candidates" is what a user will see without 
your change.

So your change has exactly the problem that you explained was so important 
to avoid, and that I explained was an unlikely corner case.