AD Item With Spell Effects???

How come there are no AD items that apply effects with spell effects?

I absolutely understand that Attack Damage has greater natural synergy with auto attacks and on-hit effects, but there are many AD based champions have abilities that apply spell effects, more specifically for AD casters.

The opposite is true for AP items. There are a few AP items that apply effects on-hit.

Okay, not many, but some is better than none.

I just don't see why we can't have both.