Why does Veigar have high base damage?

Due to his Q and his high AP scalings on other abilities, he is supposed to be a late game mage, correct? Then why, at max rank and no CDR, does his Q have 260 BASE damage on a 4 second cooldown? His W has 320 base damage at max rank but scales 1:1 with AP. I know his ult is supposed to be a single target nuke, but it has high scaling, scales off his OPPONENT'S AP, and at max rank has 500 base damage on a 90 second cooldown.