Leaching of copper using zinc
We can. 

But I see few reasons why it is not used:


Iron is much cheaper than zinc.
There can be remaining residue of iron/zinc, coated by copper, or just being excessive. While copper can be melted away and iron stays, zinc would melt together with copper, causing unwanted impurity (unless wanted for making brass alloys)
If we remove copper for environmental concerns, then by using zinc, we would just replace one evil by another. While both metals are essential for life in small amounts, both are toxic in larger amounts. ( So does iron, but at much higher level)
Removing dissolved iron from waste is easier than removing zinc.