Nashors on TF

Now, before you instantly say nashors is a noob trap, hear me out

Obviously, you need rabs, ludens, lich bane, and void staff. So, for the last item slot (excluding boots), there is no clear item. Many people argue for zhonyas, but i disagree. If you are gating into the middle of a fight rather than to pick of stragglers (and would thus need zhonyas), then your probably screwed anyway. As for rylais, tf doesnt really need the slow seeing sa he has a 2 second stun on a 4.5 second cool down. So here's why i argue for nashors

you're going to be autoing a fair amount with pick a card and stacked deck, so even if you only get two autos off in your combo (w -q - auto), you're still doing an additional .3 ap damage. .3 is not that much, but when you have like 700, that's 210 damage, which is not a joke. Though his auto range is low, im not saying sit in the back of a fight... im saying that because you're going to be autoing in your combo anyway, the procs help. plus, it is nice to have that extra bit of dps in the fight, because tf is a bit of a low damage mid laner and needs all the damage he can get.

Thoughts?