> > They are different faces, and you can also customize them 
> > separately.
> > 
> > But header-line inherits from mode-line *today*. Why?
> 
> Because they are very similar.  But the disagreement between us is not
> about the inheritance, it's about identity.  A face can inherit from
> another and still be different in small ways.

If "you can customize them separately", then they are not identical; they are
separate objects.

I don't feel strongly about this; I just thought it would be an improvement. 

I especially think it would be better to use the same foreground and background
colors - I don't have much of an opinion about box. As I said from the
beginning:

> At least the foreground and background should simply be inherited

Given that the boxed mode-line distinguishes it from the unboxed header-line (it
is also distinguished by its location and text), why not inherit the colors,
just as we inherit the fonts? 

Actually, I was really thinking of `mode-line-inactive': inherit the
`header-line' attributes from `mode-line-inactive'. I mistakenly thought it was
`mode-line', since that is the face that is inherited.

`mode-line-inactive' already uses the same colors as `header-line' (without
inheritance).

The only other attribute difference between `header-line' and
`mode-line-inactive', besided boxed, is this for `header-line': Weight: light. I
don't see the reason for that, and, frankly, I can't tell that it has any
effect, at least with emacs -Q: see screenshot. I have no problem with it; I
just don't see the point of it.

How about inheriting `header-line' from `mode-line-inactive', instead of
`mode-line'?

If you disagree, no problem - just a suggestion.