Why doesn't Irelia build more damage?

After Irelia's recent nerfs she struggles to keep her head above a 48% winrate, but I just don't know why y'all build so tanky?

I've only played Irelia a few times(never played old Irelia) and it's obvious to everyone that she has a lot of outplay potential with her high skill ceiling. It's also obvious that Irelia isn't the best duellist split-pusher like Fiora or Camille. But seriously, could it kill you to build something like;

Maybe even sprinkle some on there.

If you're cringing at the idea of that build I'm sorry Irelia OTPs I'm sorry but I just don't understand, I'm speaking from complete ignorance here. Is it because her AD ratios just can't hold up to those of other bruisers? Is it because her base defensive stats aren't high enough and her W isn't a reliable source of tankiness?

What exactly makes her inferior to bruisers like ? Is it because she lacks True Damage, %Max HP or %Missing HP damage; a reliable way to finish off the enemy?