Corki Elixir

So I was just in a game as Corki. Now, I'm not a very good Corki player, admittedly. However, I wanna know, why does it recommend ? Why not ?

: Grants 30 AD and Bloodlust for 3 minutes. Bloodlust: heal for 15% of physical damage dealt to enemy champions. Key word there is PHYSICAL After reading Corki's abilities, not one of them deals physical damage and his passive makes 80% of his basic attacks also deal magic damage. So, if a Corki buys Elixir of Wrath, he's healing for 15% of 20% of his basic attack damage from it and that's all he benefits from it with. (Note that I'm not sure how his passive interacts with the Tri Force Spellblade damage; it could be a bit better if it doesn't convert this damage into magic, however it's still not that great as that's still only 20% AD (+200% Base AD) heal).

: Grants 50 AP, 15 bonus Mana Regen per 5, and Sorcery for 3 minutes. Sorcery: Damaging a champion or turret deals 25 bonus true damage (5 second cooldown vs champions, no cooldown vs turrets).

Considering that Corki has nearly all of his abilities scaling decently well with AP, the 50 AP doesn't go completely to waste. In addition, the 15 Mana Regen is useful and the Sorcery passive is amazing. So why would he run Elixir of Wrath over Elixir of Sorcery?