Zyra's problem isn't her damage...
On the PBE, Zyra's damage has been "buffed" by reworking her plant AI. She's also had a +0.5s cc on her ult reverted. I understand that fixing bugs that grant power requires some give and take, but ultimately this won't solve Zyra's issues.
Having played her a boatload in S3, Zyra's was already an immobile champ who made up for that with her ability to shutdown a dive and punish poor decisionmaking and positioning by the other team. Since then, she's been gutted w/r/t to her mobility/utility (-10 ms, -missile speed on E, -%cdr on w, giving her less room for error in casting plants, among other things). In addition, the game has become even more defined by mobility. Very few champions that see play at higher levels don't have some sort of dash/bilnk/etc to get them in and out faster. Zyra is made of wet tissue paper and is one of the bottom 5 champions in regards to her mobility. It's gotten to the point where she's almost just collateral damage - you don't need to focus her, she'll just die as a result of you going in and casting on someone else.
If you want to help Zyra, give her some MS back and/or make her less likely to fall over from a breeze thrown her way. Until then, she's not going to be seeing serious play. And that's sad, since Zyra isn't a showy "plays" champ like the vast majority of the highly played roster.
is excellent. Very bursty, then vulnerable, exactly what a mage should be.
I think the extra movement speed is a fantastic idea to make her relevant again. She definitely needs a little sumptin sumptin.