Original Liu Kang cop.
D3 also works to avoid the iaDG.From my testing f3 doesn't work if the demigoddess is instant. Even if it isn't, you have to be holding the f3 for a long time to go under it. In that case it's kind of obvious what you're looking for there and shouldn't work that often.
What good options does Zatanna have if it's just teleport and trait? You can't really win games that way when you're just running, and she can be knocked out of trait with air tiara so that's not as effective either. So basically you can't throw rings, your trait use is limited and teleporting away is getting you any damage. How does Zatanna get me in a vortex if she can't zone effectively? Also, if you try to MB f3 a j3, WoWo can cancel into divepunch so that's not foolproof.
Zat can get trait out a lot, and WoWo will normally take a bit of bruising before she can get Zat out, as her options all have counters.
She gets damage because WoWo has to get in to do her damage. Parrying isn't getting you damage, hitting her out of trait isn't equaling the damage that Zat's got from trait zoning. WoWo has an easier time getting in but she still has to make reads and take risks to hit me. And when Zat hits you, it leads to silly setups to get more damage off you, where as WoWo has to work after she's finished a combo usually.