League of Legends (LoL) Question: Why AP Evelynn and not AD?

Because her AD ratios on her spells are about the same as her AP ratios, but since 100 AP is cheaper and easier to get than 100 AD as example, spellwise AP Evelyn is already much better (that and her ult has no AD ratio, but an AP one :3). Evelyn doesn't have that much sticking power, not enough to be able to keep autoattacking, therefore AP Evelyn is more reliable, thus AP eve is played more than AD eve :P

Her AP ratios are about the same as her AD, you can purchase more AP for your gold, her ult scales with AP and not AD, she does magic damage on her abilities, and Deathfire Grasp exists.