QSS has upgrades for AD and attack speed champions because they primarily rely on dealing sustained damage in fights. QSS lets them remove CC so they can continue to deal damage.
AP champions primarily deal burst damage and are reliant on their cooldowns. As such, they get Zhonya's Hourglass which will allow them to enter stasis and wait out their cooldowns after using their burst damage.
While there are some exceptions (i.e. AD Assassins focused on burst damage, AP champions focused on DPS), they are less common.
Another factor is that we don't want AP champions to have access to both CC-removal and stasis in an end-game build. Currently, a champion who has been hit with the appropriate CC can't activate Zhonya's Hourglass, leaving them vulnerable. If a champion could have both, then that would remove a large moment of vulnerability.
Item builds are another factor. For a long period of time, Zhonya's Hourglass was built on every AP champion at some point in the game due to how exceptionally useful stasis is. If we had an AP item building out of QSS, it would be a similarly essential purchase in most games if the stats we even somewhat reasonable for the gold value.
This is especially true for assassins/mobile champions. Imagine a champion such as Fizz with Lich Bane, Zhonya's Hourglass and an AP QSS item; how are you going to stop him during fights when he has two methods of avoiding CC (E and stasis) and one method of removing them (QSS)? He wouldn't even have to sacrifice more than a minor amount of damage to in exchange for being essentially immune to lockdown. Kassadin is a similar issues (with RoA instead of Lich Bane) since his R lets him avoid skillshots.