Why so few mages build Nashor tooth?

How many Mages do you know that rely on using AAs? Well I can think of one definitive mage at least:

He gets Passive Attack Speed from an ability and he can "AA" from serious range with his Sand Soldiers, and how quickly he can attack with the sand soldiers is affect by his Attack Speed. It could be a good item on other champions that enjoy Attack Speed but also have decent amount of AP ratios (or if they have some high AP Ratio).

stats: +50% Attack Speed +80 Ability Power

Unique Passive: +20% CDR Unique Passive: Basic Attacks deal 15 (+15% of AP) bonus magic damage on hit

most mages don't want to remain near the front that long due to being squishy. It's a lot safer to only get close when you need to cast to burst and then get back to safety. Marksmen do it because they lifesteal and heal. you see champs like teemo and such build it because their kit and soures of damage have them rely on autos, therefore nashors boosts them effectively.

it's cost is too high for somebody to invest into an item they won't be using much, I even don't really get it on because if i dont 1shot the carries, i will be too squishy to AA anyways.

edit: if you want to kill towers quickly, you are better of building in my opinion

Mordekaiser loves Nashor's Tooth, but he's not classified as a Mage anymore.

Gotta Q fast!

It is very much a melee item, though (except Azir, as he makes people melee on his behalf).

It does mess up turrets as you suggest. I split push with it on Morde constantly.

(Upvoting to balance out the downvote. You asked a legitimate question and shouldn't be punished for that.)

Teemo is the only "mage" I use it on. Makes his AA pretty powerful when you can hit someone for 50 (+30% of AP) on every AA, plus have the 30 (+10% of AP) every second for 4 seconds. Add that to the passive of Nashor's where Basic Attacks deal 15 (+15% of AP) bonus magic damage on hit, it becomes pretty devastating an item.

The benefits of Nashor's are good, as you said it yourself. The problem is the opportunity cost of taking it over something else. Most of the time, you get even more benefits out of a different item than from Nashor's. That's why so few mages build Nashor.