A big reason for AD mids taking big steamy dumps on AP is the longsword 3 pots start
AP is almost entirely limited to the Ring + 2 pots start, and while Ring is a great starter item, you're still a pot down from the start against that Zed that started longsword 3 pots.
Sure I can start boots 4, or armor 5, but I'm not going to the mana sustain I need to do anything.