AP Mages have it easy, bro. You have so many options with AP and tank that simply do not exist in the AD world. Rod of Ages, Rylai's Crystal Scepter, Zhonya's Hourglass, Abyssal Scepter, Athene's Unholy Grail, Liandry's Torment. Any burst AP mage on the spot can be decided to instead be a tanky ap character, because of the existance of these items.
Your Annie can end with over 150 Armor and Magic Resistance, and over 3000 health, while still instakilling the enemy ADC and following up on the enemy support or whoever else is still behind and weak. This is true of many mages, like Lissandra, Kassadin, and Morgana.
Some don't even need it, so I don't even want to hear crying about Lux and Xerath, who regularly carry from over 1000 range.
None of this really turns them into a Ryze (who is OP dealing over 4k raw damage instantly with risidual magic damage and is ready to burst againt 1.5 seconds later while being the tankiest mage in the game), but their oppressive utility and still burst carry like potential stacked on top of these items, is how you fix this problem you're having.