Here's my edit.

I just had to.

The hair isn't resting on the head you showed us.

I can see it now...  I ended up making the head look too tall because of the hair.

And the facial characteristics take too much space in that head-construction.

So the face triangulation would be a good example of what to do right?

Did I implement some changes successfully enough?  I also added some highlights because I want people to know Hideo has a chin and cheeks, which incidentally the same color helped with the eyes.

That looks pretty bad. But keep in mind the battle sequences are generally very
dynamic in this game, so the shortcomings are not that apperant.

They were very apparent to me.  I actually played it enough to notice why the sprites look like crap.  Actually, I think the problem was even worse in the first game, so I noticed it very quickly.  The real kicker is looking at the summons, which have far more detail put into them than most of the games' sprites combined.

I wonder if normal young gamers are bothered by this at all? Sometimes awesome quality pixelwork is regarded old and not that good looking.

Sadly, this is very true.  Young people don't have much of an eye for good pixel art or classy animations.