I want to point out Zyra's main issues. Though I want to say that while Zyra CAN Support, she IS a Mid Laner and was originally designed as a Mid Laner. This will be a long post so I've highlighted some parts in the post.
**One of Zyra's biggest issues right now is mana.**Her mana costs are colossal, for a Mid Laner or a Support.
Deadly Bloom (Q ): 95 Mana
Grasping Roots (E): 90 Mana
Stranglethorns (R): 140 Mana
Zyra's mana costs are huge. Not only does Zyra have to rush a mana item to prevent her from going out-of-mana, but her mana costs can still be an issue. She isn't necessarily a spamming Mage, but she is extremely reliant on using abilities to even access her plants. In comparison to another popular Mid Laner who is also a Minion Mancer, which is what Zyra is. Azir who is one of the most popular Mid Laners in pro player right now's mana costs are:
Conquering Sands (Q) : 70 Mana
Arise (W) : 40 Mana
Shifting Sands (E) : 60 Mana
Emperor's Divide (R) : 100 Mana
Azir and Zyra are both Minion Mancers, Mages who use others to fight for them. Similar to Malzahar with his Voidlings, they both use others to fight for them for a large amount and on Zyra and Azir's case, most of their power. While Zyra and Azir are both hugely different in their own ways, Azir is the closest champion I feel to Zyra. Both being AP Mid Laners. Azir however, is played more commonly in the LCS and one of the most popular picks. Zyra hasn't been picked since Season 3 I believe.
Zyra is one of the most unreliable Mid Laners. I don't think people realize how easy it is to dodge her abilities. Unreliability isn't something that's easy to hide and forgive on a champion. If they can't hit their abilities, then what's the point of playing them? In Zyra's case, there's almost no reason to ever be hit by her Q or E during the laning phase and against a competent Mid Laner, It can be extremely frustrating as they will always stay out of range which Zyra doesn't have much of in comparison to popular Mid Laners again like Azir or others who are almost entirely different in every way to Zyra like Viktor or Varus. Zyra doesn't have the range to match up for the delays or poor travel times/widths on her abilities.
Rise of the Thorns (Passive) : 2 Second Delay Time + 1900 Travel Time
Deadly Bloom (Q) : .625 Second Delay Time
Grasping Roots (E) : 1150 Travel Time
Stranglethorns (R) : 2 Second Delay Time
These may not seem like much, however Zyra's Q and E are her main damage aside from her plants. To compare how poor Zyra's reliability is and how easy it is to simply walk out of all of Zyra's abilities I want to compare her Q and E to other abilities.
Cassiopeia's Noxious Blast (Q) has a .400 Second Delay Time. Cassiopeia saw competitive play and was actually nerfed not too long ago because of it. Her ability is pretty similar, and the range is pretty similar too. In a target location, after a delay time, the ability activates and does damage to whoever stands in it. Cassiopeia's Q is significantly easier to hit with over a .2 second difference, this may not seem like much but in gaming time it can mean losing lane and feeding or winning lane and getting fed.
Ezrea's Mystic Shot (Q) is a good example of how poor Zyra's E Travel Time is. Ezreal's Q travels at 2000 while Zyra's travels at 1150. **This difference is noticeable and significant. **I apologize for not being able to find a more similar ability on a different champion, though this was the best I got. Ezreal isn't necessarily the best champion in the game, but he is no where near the worst and with his Q he can poke people down hard and make room for an all-in. Zyra doesn't have this luxury, not only is Ezreal's Q significantly higher in range, but it also costs less mana. Zyra cannot afford to constantly miss her abilities or she WILL go out of mana very quickly like I previously stated. Another thing is that Zyra's passive, while having almost the same speed as Ezreal's Q, has a 2 second delay on top of a terrible projectile width. For dealing up to 440 damage at level 18, while being true damage, it is very minor and will barely scratch tanks. Actually most of the time I've killed someone with my passive is due to them simply forgetting. Zyra's passive has long been considered one of the worst passives in the game due to It's unreliability and actually only being relevant when she dies.
As for Zyra's Ultimate, Stranglethorns (R) I think a 2 second delay would simply mean that if you are movement impaired, you get hit by the knockup, if you're not, then you can freely walk out of it without being in danger of being knocked up. A 2 second delay time is significant, especially without any Crowd Control, It's so easy for a person to simply walk out of the knockup. Though I will however say, the damage is instant if they stand in it, but the knockup can be extremely difficult to hit against competent enemies.
Another thing I would like to mention, though I believe this is more of a bug than an internal balance issue, is that her plants are extremely buggy. They will often not focus enemy champions, and if they leave their range they will focus minions if they are nearby. This on top of them have a very small delay after being activated, makes Zyra's plants extremely unreliable.
I apologize for the long post, though I wanted to make a clear statement on my beliefs on why Zyra cannot be viable. In my opinion, her damage is fine and she definitely has the ability to become a strong, balanced champion. Though currently I would in all honesty, consider her one of the worst if not the worst mid laners. Even Kassadin I find stronger simply due to him being more reliable, more mobile, and more tanky.