AP Carry would not have the single best utility skill in the entire game. He has pretty high cool downs on his skills with meh ratios outside of The Box. In addition, his skill set requires you to be in the middle of a team fight to do the most damage, something that's not typical of an AP Carry. The thing that makes Thresh a ridiculous support outside of his utility is that he does very good damage for a support and gets incredibly tanky for a support due to his passive.
Not changing my sig until Soulja Boy challenges me to a rap battle
-Free barriers for everyone on the team -Escape ganks with lantern -Hook to set up a kill -Attack to back enemies away or into your adc -Ult to be disruptive in team fight. -Choice to be a kill or passive lane -Free ap and armor from passive making you become semi tanky