Why does Nasus Q work on structures?
So he can kill towers like other damage rolls.
Tanky DPS are a weird class with how LoL itemization is set up.
Offensive classes mostly differ by their means of surviving long enough to deal damage.
With those defenses being Defense, Mobility, or Range.
Mobility and Range are granted for-free in a kit from essentially level 1, where if you compare the base stats of someone like Nasus to Miss Fortune - it's clear defense is not.
Which forces tanky DPS champions to build tanky.
Which means they aren't building damage.
So - to effectively be tanky DPS and keep up with assassins/mages/marksman, Riot needs to give tanky DPS essentially a free 3-major item build of defense or damage (or some mix of the 2)
In Nasus's case - he mostly gets free damage so he can build tanky, which largely justifies his Q damaging towers. Marksman and Assassins can certainly solo kill a tower with their damage items alone - so there's no real reason Nasus shouldn't be able to scratch towers.
It's also worth mentioning mages can lay down some heavy pressure on towers by fast-pushing waves and sieging teams off of towers, and that tower damage is your base AD + the higher of 100% of your bonus AD or 40% of your total AP.
Anyways - there's no real reason Nasus shouldn't be able to push over a tower by himself where all light fighters, assassins, and marksman are able to. There's also no reason a mage should be able to AA towers almost 3 times as hard as Nasus while fast-pushing waves better than everyone else.