Actually, the reason that AP mids have more access to CdR is simple: CdR is more versatile on them and can drastically impact the way a mage function.
Think about it this way: What does CdR do for AD carries?
The main effect of CdR on ADCs is to increase their sustained damage. As a class of sustained damage dealers, this is very much aligned with their primary purpose.
The ability-based utility of the ADCs that build Essence Reaver and are most successful with it is rather limited, mostly concentrated towards personal mobility or soft CCs. This is rather logical, as ADCs with a lot of utility in their spells need their damage from auto-attacks, and thus need IE more.
What does CdR do for AP mages?
Mages are based around their abilities, making decreased ability cooldowns far more valuable to them. Additionally, their abilities are not restricted to damage, but also feature strong utility effects in combination with high damage (compare to ADCs, where abilities are either damage or utility, not both).
Non-sustained damage mages (aka, burst, control and pokes mages) are defined by the fact that they are rather dangerous when their CDs are up, but lose a lot of their power when their abilities are on cooldown. These windows of opportunity are important for the enemy to be able to act upon. Itemizing for CdR makes those windows of opportunity shorter. However, for balance reasons, the mages in question cannot be as dangerous during their uptime - the power is more reliable, but less spectacular.
This tradeoff is, in essence, the reason why CdR items on mages do not feature high AP values. Or, to put it differently, itemizing for CdR pushes mages towards a more sustained threat pattern, which is not their primary purpose.
But what about sustained damage mages?
These five champions are mages whose primary purpose is to put out consistent magic damage.
Cassiopeia and Ryze both have kit-intrinsic CdR, and are thus not relying on external sources for most of their needs.
Azir is in the unique position that his sustained damage scales with both sustained damage multipliers, which means that he can make efficient use of Nashor's Tooth.
Karthus doesn't benefit as much from CdR, as his two in-fight damage tools are his Q, which already has a low CD, and his E, which is a toggle. Normally, a low CD would actually benefit from CdR more, but in Karthus' case, the cooldown of Q is so low already that further reducing it can actually diminish his efficiency - he needs the downtime of Q to move around in the fight and keep people in his E.
Anivia is a bit of an odd case, as her main sustained damage tool is also a toggle. The remainder of her play pattern is a lot more bursty, making worse access to CdR the price to pay for that.