It does, but it always does that regardless of the level his W has. That damage scales up with the levels his Q or E gets, not with the levels his W gets. The damage from those caps out when his Q and E cap out, maxing his damage at level 13. If his W gave no damage, he'd need a huge amount of power at levels 9 and/or 13 in order to justify the lack of late game scaling. The %AD removes this problem. If he didn't have this, he'd need much higher ratios or higher base damage on his Q and E. (He would need them. Just removing the %AD completely would make him a terrible champion instantly without some kind of buff). Either of those would lead to him having a much, much snowballier midgame.
Don't think about this as bonus damage he gets. Think about this as base damage and scaling that is taken off of his Q and E, and attached to his W levels. It's a good way to prevent him from being an Akali-style midgame nightmare that stops being a real champion late game.
He could use nerfs. This is the wrong area to nerf. You could maaaaybe justify taking it down to 4% per level instead of 5%, but there are so many better nerfs to choose from that would actually make him less annoying to play against. I mean, does anyone really complain about Zed's lategame? No, we complain about his annoying laning and huge midgame strength. Why not aim at those?