Should Nasus's Q be able to be used on towers?
Yes.
Nasus is a tanky DPS champion. He's supposed to deal damage, he mainly differs from assassins, marksman, and mages in that he relies on defense to survive long enough to do his job rather than heavily relying on range or mobility.
Itemization just has a really wonky interaction with tanky DPS champions in general.
Riot really should have made HP scaling standard for the tanky DPS class, we wouldn't have as many issues with marksman, assassins, and light fighters abusing tanky DPS items if that were the case.
But where mobile and ranged champions get mobility and range for free: Nasus has to itemize for his defense, which makes things awkward keeping his damage on-par with opponents that are building nothing but damage. As Nasus's damage is all kit-based: his kit-based damage should apply to structures. Full-offense in AD or AP also applies to structures, causing Nasus's turret-demolishing Q to keep things more even rather than being an exploitative feature. Nasus still has to farm up CS like any other late-game carry capable of shredding towers for his kit-based damage as well.