Why don't turrets having a slowing attack?

Damage dealt by turrets is never going to be something players take seriously unless it gets seriously overtuned. But on the other hand, if the turrets could inflict a slowing effect on Champions, then you'd have to respect their radius and not be stupid in dives.

It could be something like a stacking slow that gets significant if you get hit multiple times, though not enough to essentially root you. Heroes of the Storm's forts and keeps (but not turrets) have slowing attacks that make diving perilous, something I really like.

But I imagine Riot would hate this because it would interfere with LCS playz.