There are only 15 Manaless champions out of 110
Renekton, Tryndamere, Shyvana, Kennen, Akali, Shen, Zed, Mordekaiser, Vladimir, Rengar, Mundo, Rumble, Garen, Katarina, and Riven
Of the 15 menetioned, Shyvana, Tryndamere, and Rengar and the only ones that depend on AAing to deal damage. Out of these 3, none of them have a legitimate AP/AS build.
That leaves us with 0 champions that were prohibited from using Nashor's Tooth.
On the other hand, the few AS/AP champions who did use Nashor's Tooth, all have mana, such as Kayle, Teemo, AP Varus, AS Lulu, etc...
So who is Riot saying really needed to use Nashor's Tooth, but didnt want to pay the Mana Regen Tax?