The point of zed support is to all in some comps in level 3, but u should all in the enemy after you and your partner hit lvl 6, bcs u should have NICE ultimate combo.
It is not bad if you take poke in lane, because after you kill one of the enemy bot, you can easily burst the other one afterwards.

You can also consider tank build on support zed to be a meat shield for ur team and try to do something at the same time, but this requires that u have conq so u can do something.
Ples consider upvoting this if u are playing zed and not tryharding (even tho this way u will always win ;))