That helps them take tower? Some AP and whatnot, and a unique passive that increases damage scaling of AP when attacking tower (something like 40-50%, so maybe increase that to 80%-ish?). This can't be abused by ADCs because you need to be stacking AP in order to make use of this item.
This could be bought on AP splitpushing mages, who sacrifice combat power for more turret taking power.
JedenVojak2 votesActually it should be a melee item. Slap some AD on there and call it a day.
Ranged mages don't need help pushing towers, melee does.
18 NAKED COWB0YS2 votesbecause 
wasnt good enough
YumaS2Astral1 votesWell, Lich Bane does not synergize well with every mage.
18 NAKED COWB0YS2 votespoor you :( not having an item that works 100 percent well with every single mage. UNLUCKY
1 800 MID LANE1 votesWanna split push as a mage?
TeCoolMage2 votesthat's not going to help you take towers...
YumaS2Astral1 votesActually, because you attack towers faster (due to extra attack speed) you indeed take towers faster, thus this item helps you take towers.
That said, Nashor's Tooth has poor synergy with most mages, as almost none of them are focused on auto attacking.
A Basic Island1 voteshow would this interact with lichbane?
if the lich bane is amp'd as well it absolutely can be abused
50000000000000001 votesThat's true. Maybe just a %increase of magic damage to towers? It'll still be strong with , but not broken. I think.
TeCoolMage1 votesWell maybe then mages can do things other than stay in team fights all day, letting them get a few nerfs in that aspect so people stop complaining
Bellafiori1 voteselixir 25 true dmg per hit lich bane nashors just stop talking. if ur bad at mages and can't do both then it's not riots fault that they need to make a new item for you